Yes. The Verizon phone is sold unlocked and will work with GSM networks. Though it is unlocked, it can't access AT&T's LTE network. It works on AT&T 4G HSPA+ and lower. It can access some carriers' LTE networks.
The AT&T iPhone is locked, but you can buy a factory unlock on eBay for about $5. I used unlock_fusion and unlocked my 4S with this method. It also works on the iPhone 5.