How would you choose between these two tenant applications?

[Steve S.]

Both check out financially, credit, background check, etc. One is a divorcee with 2 high school aged children with no pets and one is a single female with a dog and a cat and no children. 

Would you let them know you have competing offers and see if they are willing to pay more?  simply pick one based on the conversations I've had with them and gut feel as well as the background / credit check (of which both are probably equally viable candidates)?

Any suggestions?