I am going on vacation for a week. Is it better for my cat to be boarded at the vet or to stay in its environment at my home and have someone come in to feed her and change her litter?

Cats HATE change!

It would be better for the cat to continue to live at home and someone come in to feed her and change the litter (and play with her for, say, fifteen or twenty minutes each time). Just be sure the cat has met and gotten to know this person for a few visits. If the cat is an escape artist, be sure to warn the helper to be careful and watch the floor when entering and leaving the house (and grab her if she tries to sneak out).

I vote for home also, then I would vote for a pet hotel, plush living for the pets,

Unless your vet is different from mine, their idea of boarding is a small cage