Can you show us a picture of one of this woman's students, or her riding?
And like you say, a good trainer is a good trainer. You don't necessarily have to like them as a person, you aren't getting married.
Go with the dressage trainer and see what you think. As a gross generalization you are going to learn more about riding from a dressage trainer and more about posing and framing from a h/j trainer.
As a h/j rider, I think I'll very strongly disagree.
Most h/j trainers/riders at the upper levels have a VERY strong basis in dressage.
Think about it. A hunter horse needs to have perfect rhythm, be supple, accept the contact, have great impulsion (via great ground covering stride and a wicked jump), be completely balanced, be dead straight and respond to completely invisible cues.
Why does that sound familiar? Oh wait, dressage.
Jumper horse needs to have great rhythm, great balance, be straight, accept the contact, accept the aids, have great impulsion and respond perfectly to the aids.
H/J only jump their horses a few times a week. The rest of the time they're doing flat work.
Now, I know there are differences between the schooling a hunter horse will do and the schooling a dressage horse will do. But the basics are all still there. You want a horse who is calm, forward and straight, you want a rider who is balanced and effective. You do the collections, the extensions, the lateral work. You use the training scale. I guarantee that almost every single horse at my barn could walk into the dressage ring today, and do well (almost because there are a few who are currently on the injury list). They may not be brilliant, but they are correct.
Many H/J coaches (including mine) have extensive dressage backgrounds.
Sorry for the tangent, but that statement was completely false and more than a little insulting.
No 'trainer' teaches how to pose. The basics are the basics, no matter what saddle you ride in.