Nope it does occasionally lag and or stutter but it's not as bad as it was prior to the latest update (for me Sprint MF9 update). Although of late, I've seen more stuttering when scrolling through the call log list.
I've only owned a 4 and 4S as my ios devices but I've owned a plethora of android devices since cupcake and I can tell you that ios is just smoother than android. I MO android is faster but iOS is smoother.
Yeah sadly it does. The difference in speed and responsiveness when going to a GE Rom and coming back to Touchwiz is really evident.
When I'm running a GE ROM the phone is consistently silky smooth, very fast and always responsive. I have never had an app force close when running GE 4.2.2 or 4.3. On Touchwiz, Google play music often crashes for me especially if I'm taking out my phone from its s-view pouch. Likewise it occasionally freezes or becomes unresponsive for a couple of seconds too. I have noticed a massive difference in memory usage between ROMs too with Touchwiz often using 500mb more at any stage than GE Rom.
I'm hoping the Note 3 with faster processor and more memory will solve the touchwiz issues for good.