I wouldn't say that a 2700 beating a 2500 is necessarily effortless. Check out the current World Cup Tournament. There are a few upsets where 2700 players are already knocked out. 2500 rating is still a strong Grandmaster. Even the games that were won didn't look like a cake walk. The 2700 players still have to play very carefully to avoid giving up counter play or a surprise tactical shot. Even though I'm only 1500, I would sooner put money on my ability to win easy against 1300 all day long as opposed to 2700 winning against 2500 easily. I do see your point about studying modern games as opposed to the older classics, because the openings are more refined, and overall, I think the level of play is more accurate. I still enjoy playing through classic games, though, for the very reason you mention, which is to imagine you are there and making history, it's a cool feeling.
Wrong ways to learn chess
Old masters games are like 2500 players beating 2200 players, without all the intricacies of modern opening theory. So in general, they are more instructive than a contoporary struggle between a 2700 and a 2300 (or 2500).
Grandmaster Versus Amateur Edited by Jacob Aagaard & John Shaw
https://web.archive.org/web/20140708091425/http://www.chesscafe.com/text/review824.pdf
Chess Master vs. Chess Amateur by Max Euwe and Walter Meiden
I'd go with the usual suspects : Morphy, Capablanca, Alekhine, Tarrasch, Rubinstein. You can't go wrong with these guys.
I confess I didn't write a balanced title to this thread. "Wrong ways..." rather aimed to drawing attention, and I'm glad if it somehow contributed to such really, really interesting replies.
It'd be mad to deny the goodness of learning from those samples of genius. But I wonder to which extent in the mind of talented children, or even elder people, it might mislead them to think that they should always play like that -almost unilaterally.
Reaching mastery involves a lot of hard and dirty struggle. Not to mention great mastery. The learning process and its principles must somehow fit the new scenarios as they come, evolving from the ideal to the real, from monologues to fights. In that sense, those eternal games aren't of much help, are they?
I feel really curious about that Chess Masters vs. Amateurs book, thanks ylblai2.
Instead of simply saying wrong ways let's first compare different methods:
1.Opening theory and tactics (the most common method)
2.A bit of everything.
3.Just tactics
4.Just endgames.
The first one is popular amongst beginners, but you can memorize a correct opening but if you don't understand it you'll just mangle the position with moves that aren't in the opening's spirit. Tactics are a great thing to study but again, require a context and plan to find. In other words you need positional and strategic understanding to obtain the opportunities for tactics.
2.A person can study attack, defense, positional elements, opening principles, endgames, etc., but where does it lead? In trying to know everything one ends up being confused and knowing nothing.
3. Some recommend just tactical study. This period will have its phase but shouldn't be first. Observation, intuition, calculation, and visualization are great things to work.
4.Endgame study. One learns to utilize pieces at their most basic and to recognize good or bad endgames before deciding on a candidate move. The fruits of one's labor are also recognized with good technique. One learns the power of the bishops, the queen's dangerous checking potential in queen endings, strategic endgames with two or one rook and a queen with many pawns on, just rook endings, bishop vs. knight, knight and bishop vs. a line king, and so on. These teach us fundamental mechanics of the pieces and coordination.
The winner here is obvious: endgame study. At least when starting out. Why is Magnus Carlsen the greatest player of all time? It is due to his extraordinary grasp of the endgame, especially rook endings and has the psychological tenacity to tire out world class opposition to blunder away draws.
I detest the endgame. A well-played game should be practically decided in the middlegame. - David Janowski 
I guess he meant well-played only by the winner!
Instead of simply saying wrong ways let's first compare different methods:
1.Opening theory and tactics (the most common method)
2.A bit of everything.
3.Just tactics
4.Just endgames.
The first one is popular amongst beginners, but you can memorize a correct opening but if you don't understand it you'll just mangle the position with moves that aren't in the opening's spirit. Tactics are a great thing to study but again, require a context and plan to find. In other words you need positional and strategic understanding to obtain the opportunities for tactics.
2.A person can study attack, defense, positional elements, opening principles, endgames, etc., but where does it lead? In trying to know everything one ends up being confused and knowing nothing.
3. Some recommend just tactical study. This period will have its phase but shouldn't be first. Observation, intuition, calculation, and visualization are great things to work.
4.Endgame study. One learns to utilize pieces at their most basic and to recognize good or bad endgames before deciding on a candidate move. The fruits of one's labor are also recognized with good technique. One learns the power of the bishops, the queen's dangerous checking potential in queen endings, strategic endgames with two or one rook and a queen with many pawns on, just rook endings, bishop vs. knight, knight and bishop vs. a line king, and so on. These teach us fundamental mechanics of the pieces and coordination.
The winner here is obvious: endgame study. At least when starting out. Why is Magnus Carlsen the greatest player of all time? It is due to his extraordinary grasp of the endgame, especially rook endings and has the psychological tenacity to tire out world class opposition to blunder away draws.
He was terrible in the endgame before about 3 years ago, oddly enough. Maybe it wasn't his study of the endgame that helped him understand the endgame.
Another reason why Carlsen is the best ever shares a reason with Coolidge for being the best president ever: the ability to do nothing when appropriate. If doing something will rack up debt then it's bad, conversely if doing something weakens your position or gives the opponent a clear plan then that's also bad.
I am not debating who is the best ever by no means but modern players have the advantage of using chess engines. How can one compare a modern player to one who never had that kind of technology to use. I am fairly new to the game and just curious ?
... No brilliancies or subtleness needed.
Perhaps you could find something of the sort that you are looking for in that Irving Chernev book. In 1999, IM John Watson wrote, "Batsford's new edition of Logical Chess: Move by Move ... is replete with advice, principles, axioms, and tips to guide one's play. ... it is definitely for beginners and players who are just starting to learn about development, weak squares, the centre, standard attacking ideas, and the like. In many ways, it would [be] a wonderful 'first' book (or first 'serious' book, after the ones which teach the rules and elementary mates, for example), ... the games are clearcut and instructive. ... almost all [are] examples of miserable defence by the loser, or of utter lack of understanding (by modern standards). But precisely for that reason, they contain powerful thematic lessons for the beginning player. My only warning would be that the impressionable student should be gently reminded by a friend or mentor that most of the rules and principles Chernev so dogmatically states do not actually have any consistent validity in real-world chess, so that the book should be looked at as a way to get started thinking about positions, not as a reliable guideline to what chess is really about. With that proviso, I would recommend it heartily to anyone just starting to explore the game, ..."
http://www.theweekinchess.com/john-watson-reviews/assorted-recent-books
https://web.archive.org/web/20140708104437/http://www.chesscafe.com/text/logichess.pdf
Reaching mastery involves a lot of hard and dirty struggle. Not to mention great mastery. The learning process and its principles must somehow fit the new scenarios as they come, evolving from the ideal to the real, from monologues to fights. In that sense, those eternal games aren't of much help, are they? (...)
I'm sorry, but I'm not sure I understand what you mean here. Do you mean that our games are so different from those master games, that we see in master games can't really be used ?
It is much harder to beat the top GMs today because defenses are so much better than a century ago. So in order to win, you have to find something that your opponent can not solve otb, which often means unusual ideas that have not been played often before. Unlike before, when practically any idea is considered a new idea.
Most of us, trying to improve, surely analyse the greatest games ever by the greatest GMs ever. In the most intimate of ourselves we wish to predict the thoughts that took place on the winning side during those magnificent displays of talent.
Isn't that a bad approach to real improvement? I mean, before getting to the excellence there is a long and uphill way to walk through.
The real point is trying to understand how they stood out from the crowd of masters until becoming individual stars.
From that basis, it should be a much more useful way to improve to study those games in which an elite GM beats average masters (say 2300-2500, even 2600) apparently effortless. No brilliancies or subtleness needed.