They both sound like they're root stock from grafted roses that were planted there and the grafts died off. Then the roots take over and grow. The red one is probably Dr. Huey. I don't know which one the white could be, there are several that were used for grafting. I thought at first R. Multiflora but I think it has too many petals for that.

Thanks. Does this mean rip them out for something better?

Those glossy leaves make me think, not rootstock. Possibly a wichuriana hybrid? Do you have any idea what kind of habit (climbing, shrub) this rose might have if it weren't being eaten by deer? I think it's going to have to receive reasonable care (sun, water, decent soil not invaded by a thousand other things) before you can decide whether it's worth keeping or not. It does look like a cultivated variety,though I have no idea which.
Melissa