I upgraded from a Strat1 to a Strat2 a week ago. The change is fantastic.
The Strat2 isn't just using a dual core CPU but the Snapdragon S4 with integrated LTE like most of the current Verizon lineup. This is two generations more recent than the A8-based CPU in the Strat1.
In Dolphin, my sunspider score is 1680. My AnTuTu score is 9443. For reference, the Strat1 scored 3307.
Battery life on idle (same apps/widgets) is much better... on the order of 2-3x better. I used to struggle to eek out 15 hours on my Strat1, and now I have 50% battery remaining at the end of a day. Just to give you an idea, my Strat2 has been unplugged for 8 hours and has 76% remaining.
Since switching to the Strat2, I disabled all radios but wifi on the Strat1 and it still only lasts 48 hours idle.
1GB RAM also makes a huge difference for me. Before, my launcher would swap out of RAM all the time, and I could basically only be running one app at a time (navigation or web browsing would frequently kill Pandora).
Other differences:
Multicolored Notification LED
Slightly thinner
Slicker back cover (I think I prefer the Strat1 for this... it always feels like it is going to drop out of my hands)
NFC
global GSM radios (I've read this in specs but can't confirm this and don't know how to unlock)
Android 4 (The changes they've incorporated into the notifications for Touchsense actually make sense)
Cellular and Wifi reception seems slightly improved
The keyboard is a little different and I'm still getting used to the comma and question mark keys. My best friend hated his and returned his for an S3, but I think it's perfectly fine.
This phone is the phone I've been wanting since I had the OG Droid and I found out VZ was bringing out LTE. It improves absolutely everything about the OG Droid. My one complaint is just that no one is talking about it (presumably not buying it either) and VZ isn't advertising it. Sucks because I can't imagine anyone choosing a Droid 4 over this, but I wonder how long rooting will take and whether any ROMs will appear.
EDIT
I don't notice a difference in screen quality.
Oh, if you're thinking about upgrading to the Strat2 from the Strat 1, there are some physical differences between the phones.
1. The camera has moved to the center of the back
2. The volume and power buttons have moved downward about 1 inch
3. The aforementioned slick cover and thinness
4. Shiny border outside of the bezel around the edge of the phone
5. Battery is a slightly different shape, has a different # of connectors, and supports NFC
The Strat1 desktop dock technically works, but because the volume button is moved downward, the weight of the phone will cause the volume to be muted when it is inserted in the dock. Also, because the phone is slightly thinner, it is just a hair loose on the dock. I've stopped using mine altogether or even keeping it plugged in all the time due to the great battery life.