They're both 1893BFLF chips, so you can swap them. Typically when it's damaged the 360 still works, ya just have no wired Ethernet, but if it's really toasted or even removed it'll throw an error, and if it's getting that hot then there's something wrong there. The best way to remove and replace it is with a hot air rework setup, and while it can be done with an iron, some solder braid and a bit of patience, using a hot air setup is a lot faster and there's less chance of casing any damage to the pads/traces under the chip. I don't mean a heat gun either, thta'll cause more issues than anything.
What ya should try, if ya intend to tackle it yourself, is remove the good IC from the spare board first. That way if ya end up lifting pads or really wrecking it you'll know what to avoid when working on the one ya want to keep. If ya trash that IC in the process it can be found online and ordered up as well, so no worries on that part of it. Removing a part is always more difficult than installing it, more so when you're trying to not damage it in any way so it can be swapped to another board, so just take your time and don't rush or pry on anything, and if it looks like ya can't get it removed/swapped there are plenty of other members on the forums that have the proper hot air setups to pull that kind of IC off there and install a new one if ya need it done for ya.