I rooted and unlocked the bootloader in my phone to try Cyanogenmod. Here's a short comparison:
Cyanogenmod 10.0 (Android 4.1):
Got rid of Samsung/Verizon crapware. I wouldn't mind the unused applications so much of they didn''t keep bugging me about updates. It was nice to have them gone and feel like I have more control over my own phone.
I didn't like Apollo. Google Play Music is a reasonable music player. Still, I can seem to play all songs of an artist in album order unless I may a playlist. Not sure why music players are so bad after all these years.
The stock Google Mail client is better than Samsung's.
The Android 4.1 calendar is a big improvement.
Generally it was nice to have the phone consistent with Google nexus 7 (Android 4.2.1 Particularly pulldown for settings shortcuts, launcher, etc.
Samsung/Verizon Stock (Android 4.0.4):
I like the phone dialer a lot better. It does speed dialing - can't understand why anyone would leave this off a dailer. Kids these days!
SMS has iOS style bubbles. Seems cleaner. I know it's copying iOS - but who cares?
Sounds are more interesting and/or environmental. I like ring tones and notification sounds that are real.
Camera application is a lot better. You can store photos on external SD.
Samsung's player has some big usability holes. Google Play Music is a better option here too.
Cell data on/off switch is easy to find and use - right there with the other features.
Bluetooth car integration works much better. I couldn't get CM 10 to handle switching from phone to media audio - every other phone call would toggle media audio between the phone filter (lower volume, no bass?) and normal. The stock 4.0.4 ROM does this perfectly.
I did a restore to the stock ROM. I like the idea of a custom, open ROM and more control over my phone, but sadly, it lacks the level of polish that Samsung/Verizon managed to produce. I'm a bit more sympathetic to Samsung's efforts to polish the Android experience, even if I disagree with some of their decisions. I'm also not completely shocked that it takes a while for them to update to Android 4.1 or 4.2, since it has to be "re-polished". I've left it rooted and the boot loader unlocked.
Still, I think Google delivers a better experience on their Nexus products, if the Nexus 7 is any indication of how their phones work. If I was buying a phone today, it would be a Nexus 4.