Yes, I also have experienced the same problems you describe.
One thing I do notice in the Mail.app package contents is that THERE IS NO SOUND FILE for fetching mail when none is found. This must be a Change in El Cap. For those worrying about not getting the "No new mail sound" after a fetch, you won't get one - because it doesn't exist! Here is a pic straight from the package contents (these are the only sound files in the package):

I played the "Mail fetch error.aiff" sound, and it is a totally different sound from the quiet beep you would get if there is no mail. It's a sound to alert you that there is TROUBLE FETCHING MAIL, not that there is no mail to fetch. The other two sounds are what is to be expected. I ALWAYS get the mail sent sound, so I am not worried about that. What I am concerned with is the erratic behavior of the New Mail sound. I have actually gotten it upon new mail arrival a few scant times, but 99% of the time nothing.
I also get the behavior where it will play the New Mail sound when I DELETE a new email as others have posted about.