Not sure if I'd call myself a pro, but I've done quite a few collabs, and as a matter of fact work is in progress to wrap up another collab, with me using Logic Pro and my collab partner using Pro Tools.
As you said, you probably have to resign to sending audio back and forth, but that doesn't mean you have to commit to something right away. What we did for the aforementioned collab is up front get a rough sense of who would roughly do what. Essentially who would focus on arrangement, who would do mixing & production, who would take what parts (e.g. leads, drums, bass).
It ended up with me doing the bulk of the arrangement work, after my collab partner started me off with a very bare bones MIDI piano part that I rearranged, restructured, expanded upon, etc. Typically I'd work on it for a bit and share a rough WIP render that we would discuss a bit about on what needed changing, and then I would work on it some more. After the arrangement was fleshed out enough, we both would soup up our parts (polishing up the midi, recorded performances, etc) and I sent over my finalised parts for my collab partner to mix.
The big reason why this works well is that we had good communication throughout the process and up front were able to divide the work without getting in each others way. That's also what I suggested.
Another approach I tried once is a bit Frankensteinian; I did a collab where I did have the DAW the other guy was using (Renoise), but I didn't feel like leaving Logic Pro and switch back to a tracker. So I simply loaded up his project in Renoise, rewired Renoise into Logic so I would have the audio of his parts in my own DAW, and simply wrote my own parts and did the full track mixing in Logic. A bit cumbersome, but it worked.
Hope it helps!