It seems that Gray Squirrels and Blue Jays don't get along. I put up a peanut feeder in late summer that is visited by four Blue Jays. Three Squirrels check the lawn below for any dropped peanuts.
Here's the fun part. The squirrels will chase off any jays if they have a chance (e.g. squirrel and jay in cherry tree at the same time). The jays in turn will dive bomb any squirrel sitting in an exposed spot (e.g. corner of garage roof).
Allowing 1 point for contact, it's Squirrels 1, Jays 0.
