From a competition standpoint the difference is that most users will effectively stay within the established platform because that's where everyone else is, which makes downloading and switching to another platform harder and in many cases it just doesn't happen.
In many ways the situation in the EU isn't different from the US, just the players are different. iMessage is an American thing, where it is quite effectively used to lock people into the Apple ecosystem and fundamentally is what Apple wants.
That's not the case in the EU, where iMessage is a side note. I'm not convinced it really warrants gatekeeper status. Here it's WhatsApp that has cornered the market, which makes it almost impossible for competing services, including iMessage, to gain traction here. WhatsApp has been designated as a gatekeeper, btw.
The problem here on MacRumors is that the reporting focus on Apple almost makes it seem as if Apple has been singled out. It hasn't. Google is a gatekeeper. Microsoft is a gatekeeper. So is Apple.
There's probably philosophical discussions to be had about the role of the state and practical discussions about whether this will always lead to the best outcomes for users, but anyone who argues that the overwhelming market position of these big tech companies and the way they use their platforms doesn't have a negative effect on competition has had too much Kool-Aid.
Are there broader political considerations about potentially helping European companies at play? Most certainly -- and why not. It's ridiculous to expect Europe not to try to help its own companies when everyone else is doing it. Why should they have a vested interest in not attacking US dominance?