Should I acept my second choice?
In this case, I would do the following first. Go to your present admin/PI and let them know what you have said here and ask them what would happen if they don't get the grant. Is there the possibility that you can be kept on with other funding, or is it absolutely dependent on the grant? 

If you are valued enough where you are, it is just possible that they can make some arrangement to keep you. "I'd rather stay, but it seems uncertain, and I have this other offer. What can be done?" 

I think it is probably worth asking the question. 

But if it isn't possible to make an accommodation, then you need to decide how much risk you are willing to accept. That is personal. It would depend on the likelihood of other options, of course.