I do both. And I teach both. You haven't given us enough info to totally answer the question, but I'll try.
FIRST AND MOST IMPORTANT - Whichever she chooses, don't try to teach her yourself if you have any desire to continue the relationship, or even get any lovin the evening after the lessons.
Skiing - generally easier to make notable progress in the first 1-2 days of lessons. Also, she'll spend less time falling down during those first couple days skiing than snowboarding.
Snowboarding - somewhere around the 2nd to 5th day, she'll have a pretty significant breakthrough and be able to ride with you down most intermediate, and probably even some easier expert runs (depends on mountain and person). It may not be pretty riding, but she'll be comfortable on more of the mountain than she will on her 4th or 5th day on skis.
I frequently describe to people that skiing has a sort-of linear learning progression, while snowboarding's progression takes a bit of a jump around that 3-5 day range and typically plateaus for a while after that (unless they keep taking lessons).
If she has spent lots of time doing sports like waterskiing (slalom, not two skis), skateboarding, surfing, windsurfing, etc., she'll have a bit of a leg up on other noob snowboarders. If she's great at soccer, tennis, ballet, she'll probably take to skiing more quickly than other ski noobs.
Bottom line though, is that if she wants to try snowboarding, I wouldn't pressure her to try skiing instead. You'll just be the fall guy when she's sore, tired and a bit frustrated after that first day (which is going to happen either way). If she does go snowboarding, I'd urge you to make sure she wears a helmet (important skiing too, but critical snowboarding IMO). Also, if she has wrist guards, knee pads and butt pads she can wear those first couple days, they'll be nice to have. Good, professional, adult lessons will also dramatically help and accelerate the learning curve. Lessons with kids will make her feel old.
One more thing. If the answer to the question "does my ass look fat in these ski pants" is yes, choose skiing. Learning to snowboard involves hauling your butt off the ground repeatedly for hours. Fat people can't do that for very long. I once had a parent ask me at lunchtime during a lesson if her son was too fat to snowboard. I sheepishly answered that he might find it less exhausting to try skiing. I felt bad because this kid really wanted to learn, but after a couple hours he just couldn't get his ass off the snow any more - and I can only haul them up so many times. And that extra padding, doesn't make it hurt any less when you fall.