whos credit will they look at more?

They will look at both. But the short history will definitely hurt the higher score. There are lots of other factors like income, work history, other assets, debt to income ratio, downpayment, etc. that go into the mortgage lender decision, but your score is really too low.

You should pull your credit report and start working on settling the derogatory items. Mortgage companies will require all negatives be resolved before you get approved. Start with the newest derogatory and work back to the oldest -- let anything close to the 7 year mark just age off.

For what it's worth, it is a very bad idea to jointly purchase a house with someone you are not legally married to. When the romance breaks up, that jointly owned house becomes a nightmare. Better one should purchase the house alone.

It will not matter, both of your scores are to low to qualify for a home loan, without a 20% down payment.

Both.