Most of our yard is covered in ivy. It makes a nice green ground cover, and we just have to trim it back from trees, beds, and paths a few times a year, which is a lot easier than mowing grass every week. Vinca is a little more insidious, so I try to remove it entirely when it shows up in flower beds.
When I saw some vinca in the ivy a couple years ago, I decided to let them fight it out. I thought the ivy had won a while back, but it must have been a seasonal surge. Now it looks like the vinca is not only holding its own but has spread out within the ivy.