Removing the right caliper makes the front wheel area appear a little cleaner while on its side stand. There's really no braking difference keeping the left over the right or vice versa.
Unless you are into some serious drag racing, I'd advise against removal of a caliper and rotor to avoid warping the remaining rotor due to the 50% increase in heat it would have to endure out on the streets. Of course, that's your call...