I'm shopping for a new road frame. I can go either way between two sizes. One would have me on a slightly shorter stem length than the other.
What do I need to consider when determining which stem length (and therefore frame size) to go with?
Do shorter/longer stems affect handling or anything else for that matter?

As far as the stem goes, changing from an 80mm to a 120mm only lengthens the lever arm that steers the bike by 15%. Regardless of where you're at in this range, you'll get used to it.

The bike with shorter top tube and longer stem will have a slightly greater amount of weight on the front wheel, due to the shorter wheelbase, not because of the longer stem.

I would try to avoid either of the extreme stem lengths like a 90 or a 130, unless you're riding a very small or very large frame. I changed to short reach bars rather than put a 90mm on one of my bikes.