Position Question

This is an interesting observation and to be honest, I'm not entirely sure either. My best educated guess is that the ending ...Bxc5 and dxc5 isn't really "less advantageous" (just counter-intuitive-looking) because White may have some compensation for the double pawns; perhaps most obvious being the open d-file when White already has a Rook ideally placed on it (d1) whereas Black has their Queen vulnerable on d8. For this reason, ...Qc7 is probably a logical follow-up, but I'm really curious to hear from other players regarding their opinions on this position as well

p.s. What I can answer though is why ...Bb4 (intending to trade pieces) and then Ne4 (avoiding piece exchanges) is likely played. This has to do with White's space advantage. To avoid being cramped, Black will naturally strive to exchange pieces (like Bishop for Knight) and White will similarly try to keep pieces on the board (like Ne4) to maximize the weight of the space advantage. 

What does puzzle me a bit though, is why does White then allow the trade anyway on c5 via Nc5 ...Bxc5 dxc5 here? My guess is what I stated in the first part with d-file compensation, but even this I'm not entirely sure as I feel like there is more than meets the eye, which I'm overlooking...

I haven't checked my lines with a computer yet, so holler if I missed something obvious.

14...Bb4 is played to take the sting out of 15. c5. After Bb8 and white lines a rook onto the e-file, a future pawn-d5 could be difficult to stop.

The reason why Bb4 is effective is because after 15. c5 Bxc3 black has full control of the d5 square, takes more center control, and forces white to babysit the d4 pawn, effectively hindering his plans.

So white plays 15. Ne4 to avoid losing the knight, and keeps the potential to fight for the d5 square sometime in the future.

With no more use for the bishop on b4, black retreats it to e7 to prevent it from becoming a target. Note that 16. c5 is not effective anymore because Qa5 b6 comes quickly, and black is able to get the queen out of harms way and start chipping away at white's extended pawn structure.

With both the c5 and d5 plans foiled, white goes to Plan C and decides to play for space with 16. Nc5. He accepts the possibility of the doubled pawns becoming a weakness for the ability to restrict black's personal space and d-file activity.

Black has to take, as after 16...b6 17. Bf5 black's weak h5 pawn could start to become an issue.

White's plan turns out to be quite strong, as after black gets the queen out of potential danger, white gains a tempo with 17. Be2, forcing a response with 17...g6. Now, white can play 18. Rd6 with a total invasion of black's privacy. 

Care must be taken to make sure white does not instantly lose to Bf5, but it appears that the threat is only superficial, as after Bd3 Bc8 and Bf4, white has an iron grip on black's position.

Thank you both for your insights, the explanations have been very helpful with understanding what is going on here.

How come 14...Bb4 is the top engine move?

14...Ng6!? and 16...Bg4 are valued as equally good, although for  the human mind the last one does not make too much sense.

https://2no.co/2DdEX6

All 3 moves are around +0.2 under close engine scrutiny, and +0.2 means absolutely nothing in human terms.

14...Ng6 was played by my friend GM Alberto David in a recent game. He lost because he neglected to play the thematic 18...b5! move at the right time (he was probably concerned about the safety of the g4 bishop, and anyway his position was OK even after delaying it for a couple of moves), but objectively Black was just fine out of the opening.

Black's DSB is just a badly placed piece (in Seirawan's words: 'it is not happy'). So we'll do well do exchange this off especially if we can double white's pawns.

Qa5 is a prospect too.