I had a 6 Plus and never had this issue really.
The only issue I've ever had (and this was with iOS 8 from day 1 as well) was that apps would just randomly quit to the home screen (Facebook was the worst offender).
I'm fairly sure that if Apple would have included more RAM in the last gen phones it would have been much better.
Back to the main issue.
I've always seen that after an upgrade/restore from backup that there seems to be strange lag/glitches.
It's always been my standard practice after doing an update, to reset all settings.
I've done this every year with every iPhone version from the 3GS up.
You won't lose any pictures/messages/app data.
You will have to re-setup any customized settings, alarms, notifications, etc.
I highly suggest anyone having these issues try this first.
Beyond that, I have upgraded to the 6S Plus and must say, the increased RAM really helps with apps not crashing and not constantly refreshing when switching back to them.
If for no other new feature, it was worth the upgrade for me.