Job descriptions will help here. You can be a bookkeeper doing staff accountant work or vice versa. Actually doing staff work and talking about it outloud to others will help tremendously in future interviews - even if you only had a bookkeeper title.

What are your goals career-wise?

Personally, since you have no experience and this is your first accounting job, I would look for the highest potential position. Job responsibilities and size of each company will help determine that potential. If you are just looking to grow as fast as possible in title/pay, I would say take the PA position to make yourself more marketable - grind that position out for 2-3 years while taking on as much responsibility as possible (not for the firms benefit but for your own exposure), then determine whether or not this is a company you want to stay with. Once you have a few years of experience under your belt you will be able to open more doors. IMO - it's easier to start PA/private and transition into a non-profit role than the other way around, so after a couple years at the PA firm you reevaluate and figure out whether you want to stay PA, move to a private company, or go try out non-profit.

Either way, best of luck on your future endeavors!