Honestly, I don't know. Never cheated, never been cheated on. All my relationship problems stem from... well, non-cheating issues, not her meeting someone new while going out with me.
Although I guess I've technically experienced a form of each of them. In the "dating a bit, but not technically in a relationship" phase, I've had a girl randomly run into another guy and decide to drop me right before our second date. I've also had a girlfriend who wasn't in love with or close to anyone else, but who wasn't mentally close to me either.
From those experiences, and assuming that falling in love with someone else would imply falling out of love with your current partner, I'd say the mental thing is worse. The first thing hurts for about an hour. The other... it doesn't fade fast at all. I suppose it's because with physical cheating, it's a one-time encounter, and the person you're with could still love you back. Usually, anyway. In any case, once they're caught, it tends to either not happen again or end the relationship then and there.
With the mental version, you end up in love with someone who is in love with someone else, which leads to weeks or months of drifting apart until things eventually break. It's not a clean "You did X, so I'm breaking up with you" thing. First you lose that spark, then things go downhill until all the little things become unbearable, and then there's a breakup over the last little trivial thing. In the end, you break up over unreturned calls or something, knowing that there was so much more wrong, but being unable to pinpoint the big cause behind it all.
Unless of course they flat out tell you "I met someone else", in which case you've basically got someone in the physical cheating category who decided to stay with the person they cheated on you with. That one just sucks.