Not sure about invasiveness, but if the vine is not evergreen, all winter the tree will look unattractive with dead brown leaves hanging all over it, because the passiflora vines like to cling at the ends of the branches.
Also from my first-hand experience, rats will eat any fruit that is available. Min.

When I lived in Watsonville I planted a Passionflower, Don't recall the variety, on my north fence. It grew great and did not frost back in the winter. One day I happened to look over the fence into my neighbors yard and saw that my plant had completely covered her hot tub/spa. I went over and apologized and offered to remove it. She said NO she loved it! The next year was cold and it was burned to the ground. I would not plant a Passiflora unless I was in a reliably frost free area, and was willing to prune as needed to keep under control. Al

SFGuy,

Both parents are montane tropical forest denizens, I know that P. parritae is quite restrained in its growth habits (heat kills it rather than spurring more growth - I received one and lost it in an unusual April heat wave [90+ degrees for about two days] a few days later) and the other parent is likely to be as well. I really doubt that it is likely to get away from you the way lowland cousins like P. edulis will. Your link says "more vigorous" than P. parritae - it would be hard to imagine a passionflower less vigorous!

Ryan

Check out the size of the parent species at the SF Botanic Garden and judge for yourself; they do get quite large where conditions are favorable such as SF and coastal influenced mild northern California locations. Even here, they can suffer in a west or south facing exposure in a rare heat wave.

If you live in SF, 'Mission Dolores', which is the antioquiensis X parritae hybrid you are talking about, will be a good grower. I grow all three (parritae, antioquiensis, and 'Mission Dolores') here in coastal Southern California and the parritae has the least trouble with our rare heat waves. It is also the strongest grower of the three and has completely overgrown two large old orange trees and other parts of the yard. 'Mission Dolores' is the second best grower, but is more open and less inclined to branch. P. antioquiensis is the most heat sensitive of the three for me. How well they grow for you and how large they are going to become will depend almost entirely on your climate. If you are in the city, antioquiensis is going to be the smallest when mature, and both parritae and 'Mission Dolores' are going to become very large vines unless you prune them. They are not going to really be invasive, but they will get quite large. As long as you don't overdo it they tolerate pruning fairly well and bloom on new growth, so if you prune in the fall you don't really lose a lot of flowers.