Only the flowers have a resemblance, the leaves are quite different. Crossvine has smaller flowers earlier in the spring/summer, not blooming much past the middle of July. Campsis is just starting to bloom at this time.

The leaves are 2 leaflets to a petiole on crossvine, whereas Campsis has 5,7 often 9, and the serrations are much deeper. Campsis prefers drier ground. Both root from layering, but the biggest difference is that Campsis will come up 20 ft (or more!) from where it is planted. Crossvine is also evergreen in the South, but Campsis never keeps the leaves. I'm certain there are other differences, this is just a start. Both are native to the US.