Dear Hristodoulos,
Well, we Eastern Catholics believe we are FULLY Orthodox since we do commemorate the Pope as was done during the first millennium of the Church - as the Administrator here says, "Communion with Rome is the Crown of Orthodoxy." (Believe it or not . . .).
St Peter went throughout the East, consecrating bishops and founding Churches. He is more of an Eastern saint than a Western one, since Rome in the West is the only place he set up a church, as I understand, and, of course, was martyred there.
But we simply feel RC's are wrong in appropriating him all to themselves. It is better that the See of Rome claim primacy on the basis of St Peter being there.
If the East were to follow a rule like that, we'd have all kinds of primatial sees based on St Peter beginning with Antioch etc.
When it comes to the doctrines that RC's confess, we EC's let them have their way, as long as they don't impose their narrow scholastic ideas on us (see the long-winded thread on the Filioque - the recent one).
As for the Immaculate Conception, we try not gloating about the fact that the East affirms the total holiness of the Most Holy Theotokos and never even considered that issue a problem.
It is difficult to be in communion with RC's, we must admit. They can be arrogant, at times, and think that their way of doing "church" was the way it was done from the very beginning.
If you challenge them on any of this, they will get their Latin backs up against the wall, demand references, pretend they don't see them when you do, accuse you of implying tendentious interpretations and denying reality, then they will come close to calling you a heretic/schismatic while all the time affirming that "our unity is almost complete!"
This is why I would never leave the EC Church for Orthodoxy.
You Orthodox have it easy! It is a much greater asceticism to try and live with our cantankerous RC brothers and sisters, having to put up with them in all meekness and poverty of spirit, without resentment and to be always fighting the urge to just go away so as not to have to listen to them . . .
That is the truly Orthodox ascetical way, as I read the Philokalia . . .

Any other questions?
Alex