Did you reload the same apps back onto it after the reset?
If so it's highly likely that it's something installed that's causing it to lag. I would do another reset and load applications slowly, reinstalling the apps you have had the longest first as they are less likely to be causing issues.
You could also install something like OSMonitor which will tell you what is using the processor. See if anything is using loads of CPU.
Same thing happened to me, and I also don't like cases at all.(manufacturers go to extreme time and effort to make a nice design and slim dimensions, so it seems a waste to put an ugly plastic case around it.) So I just put a nice carbon fibre skin on - this is the one I bought if you're interested :) http://www.amazon.co.uk/Textured-CARBON-Sticker-Protector-XPERIA/dp/B00LZOB5OU/ref=sr_1_1?ie=UTF8&qid=1432211660&sr=8-1&keywords=xperia+Z2+carbon+fibre+skin
Have a look at Juice Defender as well. It will monitor the Battery life and can extend the battery life.