You misunderstand the question @fixing_the_hole. 1.e4 IS drawish when white wants to play for a draw. The Petroff and Berlin are openings when black wants a draw so are unrelated.
At least, this is the commentary I've heard: that black can be frustrated when white goes 1.e4 and tries to suck all the play out.
Thats correct that there are lots of potential forced draws that white can play into after 1.e4, but white can ALWAYS play that way regardless of what first move he chooses. If white wants to play like a coward, many times there is little that black can do besides trying to bait white into a mistake. And I think you might be the one misunderstanding the OP's question...as he is trying to figure out whether its better to play 1.d4 if you're going for a win, and if you're strictly playing to WIN as white, you play 1.e4.
Your last sentence is just not true about modern chess.
1. d4 allows better chances to create complications and to create positions in which both sides maintain greater chances of pawn tension and flexible pawn structures.
1. d4 allows better chances to play for favorable endings and less forcing variations are to be encountered than what Black can choose after e4.
1. e4 and the e pawn is hanging and Black can always strategically target the e4 square.
1. d4 makes no such consession and the fight is postponed until later in the game.
1. c4 Kicks the fight until even later than does 1.d4 but does not offer as much flexibility for White due to the Black response of 1. ... e5.
1. e4 remains the preferred move of dogmatists, no doubt.
I know you're a better chess player than me, but I'd be curious how white can better play for a win against the QGD/Slav/QID/Ragozin than any of the 1.e4 lines. I understand the idea of tension, and it can be easier to prevent exchanges of pieces within 1.d4 lines, but the initiative after playing 1.d4 seems easier blunted.
Great posts, thanks! Thinking of the Petrov and Berlin, I've heard that the King's Gambit fell out of popularity at the top level because Black no longer has trouble equalizing.
I think its mainly because black has so many choices to play against the KG, and they are ALL good. Of course top-level GMs are extremely prepared, so for us non-titled players the Kings Gambit is a fun practical weapon. And it still CAN be played it that top level...there have been lots of white victories at the highest levels of chess over the past 50 years. Spassky beat Fischer with it, Short beat Kasparov with it, Judit Polgar even beat Topalov just 6 years ago! These are world champions who have lost to the King's Gambit. Play what interests you bud