When I moved from westen Canada to eastern Canada we drove through the USA and crossed with our cats. We weren't even asked for paperwork at either border. Flying is a whole other ballgame. My cat was a basket case when it arrived in the UK from Canada - I know that was a long haul, but even so, a pet in the cargo hold (albeit heated pressurised hold) with all that noise and no human around?
IMHO driving is definitely way less stressful on your pet.
If there was no other choice and it is little and you could fly with it under your seat it wouldn't be quite that bad, but it would have to be a mite!