I doubt that the EO version will be adopted as the official version, as I don’t really see how the non-inclusion of CVS2 in Evo X (which I hope wouldn’t happen) is relevant. Fact of the matter is, if ever, CVS2 won’t be at Evo, thus neither the PS2 version of the EO version regardless of backwards compatibility will make it at all. It boils down to what people are used to and prefer at the moment, which is generally speaking, the PS2 version.
So to answer your question, I don’t think that the EO version will be adopted as the official version. For one, as mentioned already, people are already used to the PS2 version and second, the XB/XB360 aren’t big over in Japan so it’s nigh-impossible that the people over there are going to pick EO over the arcade version. Simply put, as long as there are working PS2s and copies of CVS2, EO becoming the official tourney/competition version won’t happen.
Regarding tiers… they’d be pretty much the same, I think. It’s not like Bison loses his PTF in the EO version, or other characters their really good normals and customs. P-Groove gets moved up, I think, because of Super Cancels. (which is another reason why people will probably shy away from the EO version)