+1, I do exactly this and have a slim in the lounge and an Elite in the bedroom so EXACTLY the same setup
Just put your profile and saves on the stick and move it between consoles. The only thing I've found is Crysis 2 glitched on me so I put the save on the HDD. I went to play it on the other 360 so just deleted the old save on the stick and copied the new one over and then onto the HDD of the other console. You shouldn't have to do that though.
If you're using both a lot, I'd recommend a decent USB stick. I use an 8GB OCZ Rally2. Fast read and write and very reliable.
Hopefully for the next xbox, Microsoft will change how this works as lots of people have more than one console. I sometimes get into bed, fire up the xbox and realise the USB stick is downstairs