I personally find it distressing that so many Armenians, including some of our clergy, have such a liberal attitude toward the Catholics. True, we have much in common with them, just as we have much in common with some Protestants, but the differences we have are significant. The Ecclesiology, as you mentioned, is one issue, and I think it is a bigger issue than some people realize.
I think most Armenians don't realize that being officially in communion with the Catholics would be an entirely different thing than being in communion with our sister Churches, like the Copts or the Syriac Orthodox. Rome does not have "sister churches." Rome has "daughter churches." The only way we could officially come into communion with Rome is to become a daughter church, which would really change what our Church is. People don't understand that, though. They think that if we go into communion with Rome, it would be like being in communion with the Copts: No big change. They are wrong about that though, and it distresses me that our clergy do little if anything to properly educate people on that.
Aside from the ecclesiology, there are other theological issues. Granted, these are obscure, but they are not insignificant. We don't believe in the Filioque, and their Christology still bears some Nestorian influences. From what I have observed, the EO's have done a much better job of reinterpreting Pope Leo's Tome and Chalcedon through the Christology of St. Cyril than the Catholics have done. (Note: I do not want to get into another debate with the Chalcedonians on Christology. Any attempt to turn this into such a debate will be kicked into the private forum.)
There is a reason Cilicia's union with Rome fell apart. St. Krikor Datevatsi and St. Hovhan Vorodnetsi knew what they were talking about. They did not oppose union for the sake of being contentious. They were among the best theologians the Armenians ever had, and they saw real differences between what the Catholics teach and what we believe.
That being said, I can fully see what attracts so many Armenians to the Catholics. They have historically been much more friendly toward us than the Greeks and Russians. Not being "next door neighbors" with any Catholic nations means that we have not had any wars with them, nor have we ever been militarily occupied by them. Armenians look at the mistreatment we received at the hands of Byzantine emperors and that we received under the last czar, as well as the current hostility we get from the Greek monks at the Tomb of Christ, and the horrible things done by HH Ilya of Georgia, and they compare that to our relatively pleasant dealings with the Catholics. Those are the things that laypersons look at, not the theology. So I can see how so many Armenians think we are the same as the Catholics, but different from the Greeks and Russians.
Theologically and ecclesiologically speaking, though, we are much closer to the EO's than to the Catholics, and people do need to be educated about that. If we are to ever heal any schism, it would make sense to heal the schism between us and the EO's before looking toward the Catholics.
People don't see that, though, and the clergy are doing little to educate them. When our clergy hold ecumenical prayer services and practice intercommunion, that gives people the false impression that there is no difference. This leads people to fall away from our Church and join the local Catholic parish that is closer to them than the nearest Armenian parish. After all, if we commune Catholics and we have joint prayer services with them, that means we are the same. And if we are the same Church, why should a person have to drive forty minutes to the nearest Armenian parish, when there is a Catholic one five minutes away? I've known people who have effectively dropped out of the Armenian Church for precisely this reason. They have no intention of leaving the Armenian Church, but they stop going and join a Catholic (or even a Protestant one) because it is more convenient and they've been led to believe we are all the same.
Whatever. Sorry about the rant. It's just that this is a frustrating issue, and I think our Church's leadership needs to do more to educate people about what separates us from other Churches, rather than give people the false impression that we are all the same.