A crossover? Well, assuming it's 1 brief event, & something, like, say, a movie... well, for one, it'd probably ignore our systems, because crossovers, drama, etc.
An encounter between the two settings.... I imagine the initial conflict would come after some discovery & interactions; The 2 settings finding out about one anothers' worlds & inhabitants, ways of life, ecosystems, etc.
Based on what I've seen, I imagine they might perceive each other as:
For how Pokemon views Digimon, too separated, as the Digital World is kept secret & separate from their setting's human world. Of course, this has its benefits, keeping out danger except from the bigger threads, & some prefer that way.
Whereas with Pokemon, the Digimon setting might perceive them as overly controlling & abusing; Most every human interacts with Pokemon, commanding them in battles, in contrast to the more independent Digimon. But most humans aren't malicious, some Pokemon prefer this, & their setting benefits greatly, with incredible technology, usually peaceful, & happy inhabitants.
The resolution of this conflict would probably be as they realize the benefits of one anothers' systems & why they are the way they are; Status quo is God, after, all. But that'd be a bit of an anti-climax?
Perhaps at some point, there may even be a tournament or such. Possibly for the spectacle to this crossover's viewers, & in-setting, as a show of goodwill & understanding towards one another in-universe.
Nonetheless, though, I think what's most likely is something like this:
During the tourney or learning of one another, the less kindhearted of both sides join & collaborate together. Amassing Pokemon, & using them to take control of more Digimon, striving to seize control of all three worlds: Human Digimon world, human Pokemon world, AND the Digital World!
As realization of this occurs, everyone realizes they have to set aside their differences, & band together to stop this common enemy. The Digimon must work with the humans & the Pokemon must work with the Digimon, who are so alien & differently thinking to them.
As they come to understanding of each other, & fight in combat, since this is a crossover of 2-merchandise-heavy settings, a new, super powerful, super merchandisable form appears. Likely, it would combine the elements of Pokemon & Digimon. Their battle readyness, bond with humans, & perhaps a new form of evolution. I imagine something that rapidly or reactively evolves during battle in small ways that it can revert, but in crisis, changes drastically, these changes being those that approach towards its final form, with the less beneficial discarded.
Perhaps during this conflict to stop the seizing of all 3 worlds, the "interdimensional pathways" that enabled this meeting of masses would start to... destabilize or the like.
As the conflict is resolved, & the settings come to resolution with one another's ways, & have survived a great conflict, they quickly realize that they can't stay together forever. Those that wish to leave or stay have to choose now, & most choose to go back to their own world.
As the connection ends, so, too, does the crossover.
(I hope I did good.)
