Which style of play is better?

Is it better to allow an opponent to trade material with you while developing other pieces, or to trade pieces just as vigorously, assuming you had to trade material because of your opponent's playing style?

The way I figure it is, if you allow your opponent to trade material, he's giving up pieces he's already got developed for your pieces, whether developed or not. That gives you the turn he spends positioning his pieces to take yours to develope another piece.  Unless he's particularly crafty, he probably won't be able to halt piece developement and threaten your developed pieces with one deft movement.

On the other hand, if you trade material with him as much as he does with you, that is, if you attack his pieces with the same ferocity that he attacks your pieces, then you both chip away at each other relatively equally, until someone makes a double play. That means that inevitably unless you trade absolutely everything, one of the players is going to come out on top; perhaps you or perhaps your opponent.

Personally, I think the first option is more profitable to you than the second, but I guess I'm just not experienced enough to properly compare and contrast the two. I'd like some input from you all and your opinions, but please keep them intelligent and please give some reasoning behind your position. Thank you!

Its all in the style - AND THE GAME! There is no good answer to this post..

It's all in the position, sometimes in your opponent's skill. If you opponent is a poor endgame player, you could trade away as much as possible, and in an endgame where you are a pawn down, you could still come out on top.

Let your opponent trade as much as he wants. Development is usually more important than trading.

depends on the position. If you are putting pressure, don't exchange and if the other way round do exchange

One of the fundamental elements of chess is Time. If he is losing Time by moving his already developed pieces and trading for pieces that have not been moved much, you are gaining Time. If the game is open then those extra tempii may be of real use to you, if you are a skillful player.

Of course you still have to evaluate the position at hand.

I’m just gonna use a BUMP

Attacking chess is the meta below 1800 for sure, it is the principled way to play chess below 1800 because your opponent is almost always is behind development, makes suspicious moves that lacks central control, king safety is horrendous in the opening and is punished by attacking and making threats.