Can't say I watch too much 1080 video on my phone (do most of my video watching on my Note 8 tablet), but MX Player is what I use too.
The HTC stock player has always been a joke. Its not compatible with a lot of formats/codecs, I've never really made any use of it aside from watching the videos I've taken with the phone's video camera. In general, I've never been much a user of stock players from any manufacturer. There is always going to be incomplete format support and/or performance lag. I'm guessing its due to licensing of various proprietary formats/codecs. Good 3rd party players are the way to go on Android.
Why the stock player lags now on Sense 5, when it didn't before, I can't say for certain. Lots has been updated in Sense 5, but HTC seems to break as many things as they fix sometimes. So this may be one of those cases. I haven't read about this issue before, so there is likely no easy fix.
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Phone: AT&T HTC One (M8)
Tablet: Samsung Galaxy Tab Pro 8.4 (WiFi only)