I really would do both.
I work in HR and this happens quite often. We are happy for the people who make a better decision for themselves.
Our Orientations are only held after references have been checked, background checks are completed, and there has been a formal offer for employment. They last 4 hours, at least. The only bummer is spending that much time on someone who may not work out, but like I said, it happens.
You seem to have two opportunities to choose from. I would give yourself a chance to check them both out. That is the only way you will know which will be better for you. And, in this hiring climate, we've hired people and ended up not having shifts for them after all, in which case, we never hold it against anyone for finding a better fit.
You are in an optimal place. If you may have two opportunities to choose from, take advantage of that. Get a feel for which will be a better place for you and go from there.
It's a very simple concept, but get a piece of paper and write the pros and cons for each position. Which one will have the more pros for you.
Just my opinion and best wishes.