user27380: Stockfish evaluates this as advantageous for White (+0.6 at depth 22), with Bxe4 being the only move retaining the advantage.
Why is this so good for White?

We give up the bishop pair
We're left with the bad bishop vs the opponent's good bishop

Even after 1. Bxe4 Qxe4 2. Qxe4 dxe4 which looks like a textbook good bishop vs bad bishop scenario, Stockfish thinks that White is better (+0.2).
Why is Bxe4 the best move and why does it lead to an advantage for White?
    [FEN "r3q1k1/ppb2p1p/2p3p1/2Pp1B2/1P1Pn3/4B3/P1Q2PPP/4R1K1 w - - 0 1"]


user15049: Bxe4 does not lead to a permanent advantage for white, but Bg4 or Bh3 also do not.
The position is static (blocked center pawns, no passers, one open file) and the bishops are not that good in such positions. The Ne4 is as good as the Bf5. After Bxe4 Qxe4 Qc3 white has a bit more due to the control of the e-file (which is based on quite abstract tactics) and due to his qualitative majority on the queen side. His heavy pieces are more active. But black can neutralize this with careful play.
I am pretty sure that many GMs would actually avoid Bxe4 and play Bh3 or Bg4 instead, so you are right if you are doubtful about Stockfish's suggestion. All three moves, Bg4, Bh3 and Bxe4 are playable and of comparable quality. And none of them gives white a relevant advantage.

user8860: We can't read the engine's mind.  The evaluation is the result of calculation to depth 22, i.e. looking 11 moves ahead; the main line(s) after both 1 Bxe4 and White's alternatives should give some idea of why the engine gives White +0.6 here and why the alternatives (mainly Bg4 and Bh3) are worse.
Looking at it without an engine, we might guess that after the trades on e4 White has a worse Bishop but more space and a Queenside majority -- and no more worries about a Black attack on the Kingside.  After 1 Bxe4 Qxe4 2 Qxe4 dxe4 White can move the Bishop outside the pawn chain with tempo (discovered attack on bPe4), and 3 Bg5 also controls d8 so that after Black defends the pawn White can continue 4 Rd1 and 5 d5, curing the d5-hole (White doesn't want to see Black play Rd5 or Kd5), start getting the Queenside pawns moving, and maybe use the d-file.  White also has the option of not trading Queens and instead trying to use the e-file with something like Qd1 (Black won't play Re8 because then Bd2 wins).
If Black answers 1 Bxe4 with dxe4 then White seems to win the e-pawn by moving the Bishop (2 . . . f5 doesn't help Black because 3 f3 and the pinned pawn falls); then the "+0.6" might mean that Black has some compensation thanks to the better Bishop.

27380: <p><a href="https://lichess.org/analysis/r3q1k1/ppb2p1p/2p3p1/2Pp1B2/1P1Pn3/4B3/P1Q2PPP/4R1K1_w_-_-_0_1?color=white#0" rel="noreferrer">Stockfish</a> evaluates this as advantageous for White (+0.6 at depth 22), with Bxe4 being the only move retaining the advantage.
Why is this so good for White?</p>
<ol>
<li>We give up the bishop pair</li>
<li>We're left with the bad bishop vs the opponent's good bishop</li>
</ol>
<p>Even after 1. Bxe4 Qxe4 2. Qxe4 dxe4 which looks like a textbook good bishop vs bad bishop scenario, Stockfish thinks that White is better (+0.2).
Why is Bxe4 the best move and why does it lead to an advantage for White?</p>
<pre><code>    [FEN &quot;r3q1k1/ppb2p1p/2p3p1/2Pp1B2/1P1Pn3/4B3/P1Q2PPP/4R1K1 w - - 0 1&quot;]
</code></pre>
 15049: <p>Bxe4 does not lead to a permanent advantage for white, but Bg4 or Bh3 also do not.</p>
<p>The position is static (blocked center pawns, no passers, one open file) and the bishops are not that good in such positions. The Ne4 is as good as the Bf5. After Bxe4 Qxe4 Qc3 white has a bit more due to the control of the e-file (which is based on quite abstract tactics) and due to his <a href="https://lichess.org/study/t1hfUeFZ/fIa1mGb5" rel="nofollow noreferrer">qualitative majority</a> on the queen side. His heavy pieces are more active. But black can neutralize this with careful play.</p>
<p>I am pretty sure that many GMs would actually avoid Bxe4 and play Bh3 or Bg4 instead, so you are right if you are doubtful about Stockfish's suggestion. All three moves, Bg4, Bh3 and Bxe4 are playable and of comparable quality. And none of them gives white a relevant advantage.</p>
 8860: <p>We can't read the engine's mind.  The evaluation is the result of calculation to depth 22, i.e. looking 11 moves ahead; the main line(s) after both 1 Bxe4 and White's alternatives should give some idea of why the engine gives White +0.6 here and why the alternatives (mainly Bg4 and Bh3) are worse.</p>
<p>Looking at it without an engine, we might guess that after the trades on e4 White has a worse Bishop but more space and a Queenside majority -- and no more worries about a Black attack on the Kingside.  After 1 Bxe4 Qxe4 2 Qxe4 dxe4 White can move the Bishop outside the pawn chain with tempo (discovered attack on bPe4), and 3 Bg5 also controls d8 so that after Black defends the pawn White can continue 4 Rd1 and 5 d5, curing the d5-hole (White doesn't want to see Black play Rd5 or Kd5), start getting the Queenside pawns moving, and maybe use the d-file.  White also has the option of not trading Queens and instead trying to use the e-file with something like Qd1 (Black won't play Re8 because then Bd2 wins).</p>
<p>If Black answers 1 Bxe4 with dxe4 then White seems to win the e-pawn by moving the Bishop (2 . . . f5 doesn't help Black because 3 f3 and the pinned pawn falls); then the &quot;+0.6&quot; might mean that Black has some compensation thanks to the better Bishop.</p>
