When you recover your gamertag, what you're doing is copying the current status of your gamertag from Microsoft's servers to the console where you're recovering it (your gamerscore and achievements).
Often, this will give you the information you wanted to restore, but keep in mind that what you are recovering is your gamerscore and achievements from the last time you were online. You will not get credit for any achievements you got offline if you did not sync them by going back online on that console prior to recovering your gamertag on your console. (The same will be true for cloud saves: you have to save your game back to the cloud in order to access it from another console.)
As James mentions, and as this question points out, you can easily move your profile back and forth between consoles by saving it to a USB stick (or to a memory card, if you both have older 360s that accept them). You would not need to recover your profile each time, and if USB slots are a problem (if you're playing a game that uses several of them), you can move your profile to the hard drive of the console you're playing on, and before you leave, you can move it back to your USB stick.
If you do that, keep in mind that profile and local save games are not necessarily saved in the same place. If you want to take your saves with you, you need to save them in the cloud or on the USB stick.