What is White's advantage in this position?

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koenvv

I was playing White in a classical game and we got to this position (after move 12). I know my moves were fine up until 13. Ne5, which I do realize was inaccurate and I thought about 13. Qe2 for a long time. The thing was that I felt like I had a small advantage, but I didn't understand where this advantage was (after 13. Qe2). 

You can ignore everything after move 13, my opponent (rated 1576 OTB) made a stupid blunder, but I'm not happy with how I played it after the opening either.

Could anyone share their thoughts on the position and tell me 1. Why the position is better for White and 2. How you could best use this advantage.

Thanks in advance

tygxc

13 Qe2 or 13 O-O were better indeed. 13 Ne5 moves your knight for a second time while you have not yet castled. 13 Ne5 initiates trades that throw away your small advantage.
Your small advantage consists in trading your bad bishop Bg3 for his good bishop Bd6, so you are left with a good bishop Be4 against his bad bishop Bb7.