why d4 is better than e4

Everyone in this forum has lost to both opening moves.

I read the articles when they were published and glanced again after your link. His conclusion that the differences are so slight that it's not worth changing your repertoire seem on the mark. The statistical gymnastics he performs to make e4 come out slightly ahead, OTOH, should be taken apart by another statistician. I have a vague sense that he missed the forest for the trees.

Super repetitive, super closed, super boring.

Most Super GMs play d4. They know best. For FIDE rated games, I play d4. chess com games mostly e5. d4 gives black limited counter play.

They're both tactical and they're both strategic. Games are made open or closed, sharp or quiet by all the moves that come after the first...not by the first move itself. 

What makes this even funnier is that the OP deleted his original post.

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Kasparov used to favor d4 whereas Fischer e4

They know best what a super-GM should play against another super-GM. But what does that have to do with the question of what one patzer should play against another patzer? 

Apples and oranges.

Most Super GMs also play e4. Such as Carlsen, Anand, Caruana, MVL, Navara, etc.

Reading Masters of the Chessboard recently, I came across what I think to be patient zero for the whole "e4 = tactical, d4 = positional" thing

"The openings beginning with 1.e4 e5 are more apt than others to lead to open positions, since as a rule d4 and exchange of centre pawns will follow. On the other hand it is obviously more difficult to carry out the move 2.e4 after 1.d4 inasmuch as the square e4 is originally unprotected. This is the reason why d4 openings as a rule lead to closed positions"

So, first thing, he says that e4 e5 SPECIFICALLY has a higher probability of open positions - not 1.e4 in its entirety. Second thing is that 2.c4 is played precisely because it gets around the need to play e4 in order to break the center. The exchange variation in the QGD is a structural cousin to the open Sicilian (with colors reversed) where c pawn is traded for d in order to resolve the structure and create a more open game.

I just want the chess playing community to think a little more holistically about these two moves. They're different - no question - but the commentary in your head shouldn't read "1.e4! Seizing the initiative, white is better" "1.d4? Seizing the defensive. White plays for long term advantage."

In the Exchange Variation of the QGD, the c-Pawn is traded for the e-Pawn, not for the d-Pawn.

Who answers cxd5 with anything but exd5 in the QGD Exchange?

It's the colors-reversed analogue of the Caro-Kann Panov Variation (1. e4 c6 2. d4 d5 3. exd5 cxd5), not of the Sicilian.

actually cxd5 Nxd5 in the QGD exchange is really annoying to play against, especially for a win

That line plays like a Gruenfeld, not like a Sicilian.

Kramnik does! My database has 15k games from 4.cxd5, and 14k play exd5, but Nx has been played over 900 times, mostly by Kramnik and Dominguez-Perez (at top level). But you are right.

Because it's not