I'm in the exact same boat as you, my friend.
I had to get my TSMC iPhone 6s serviced at the Apple Store..they couldn't fix the issue I was experiencing, so they gave me a replacement. As soon as I walked out, I checked which chip I had, just out of curiosity. I wasn't so much worried about the battery life anymore, especially with the newer studies and tests proving not much of a difference. But, just as a tech geek, I was curious. I saw it was Samsung...shrugged....and went on my way.
My phone is newly set up...not restored from backup...and I get heavy delays and lag as well...when I unlock my phone, it takes 2-3 seconds for the status bar to display and for the home screen to become responsive.
I don't have a passcode on my phone...sometimes when I swipe to unlock the device...the time on the lock screen will slide out of view...i'll sit there and wait a few seconds looking at the screen...before it finally starts to load up the home screen.
Yes, I've restarted...yes I've reset/erased/started over...it doesn't matter. I definitely notice this too...it's very disappointing given that this A9 chip is supposed to be blazing fast..and with 2 GB's of RAM alongside it...but, no..it's laggy and feels like it's trying to catch up to your finger gestures/motions.
The one thing I can say, however, is that my battery life has been just fine...I haven't noticed any difference at all in that regard...battery life is great.
But yeah...very delayed, laggy, sluggish...and most importantly..disappointing (given the device retails for over 850 dollars)