Well, if they are both carrier branded devices, and different carriers, and the devices are stock, it probably isn't going to work. Not initially. If they are both the same carrier, then you should be ok. Just pop in your sim at the store and check before buying.
But if it's a different carrier...
First, you will need to "unlock" your new device, so it will operate on other carriers networks. There are sites you can google that do this, and they are not very expensive. Basically they send you the unlock code to enter into your device. Google hard enough, and you might find some for free.
If you really sweet talk the girl at the carriers office where you buy the phone, they may do this for you there, as it's totally legal. Tell them you travel abroad quite often, and you need it unlocked. Flowers, sweets, the usual stuff.
You are correct when you run another carriers sim, you probably won't get some features, but I would suspect you will get 3g, 2g at the very least.Wifi should be ok. Probably won't get OTA updates.