Just to offer some insight, I've got a fresh installation of Raspbian Jessie with Pixel, and RetroPie 4.0.3 installed on a test Pi 3, and it's great. The new desktop is fine and reasonably swift, and RetroPie is fine.
I also performed a dist-upgrade on my main Pi 3, which was running Raspbian Jessie from the May 27th image, and had RetroPie 3.8 on it. This system had a lot of additional software, including a custom ffmpeg and retroarch build for RetroPie recording, along with monodevelop, VPN, kodi, and loads more, built over five months.
After the update the desktop suffered from random reloads of the main menu bar, but the worst effect was a noticeable lag when dragging windows around the screen. Moving Chromium around felt like the window was connected to the mouse by elastic (the rubber-banding effect in Daytona springs to mind!)
I'm currently restoring a backup. I think the only way forward, with a view to having a stable , reliable, system, is to manually rebuild the entire installation on the new Raspbian base, as I've no idea what's underlying the odd performance and stability issues. This seems to be a general rule with o/s upgrades on most platforms...