As Cyrillic and Mabsoota's posts have shown, there is some difference of opinion or point of view in this matter.
For instance, my priest, who is in no way an extremist, has stated in no uncertain terms that we will not under any circumstance be communing Chalcedonians in our church. At the same time, however, when the Copts first came to this area in the 1970s-80s, before there was a church for them, at least some of them used to commune at the local Greek Orthodox Church (with the Greek and Coptic bishops' full knowledge), as it was the only option in town. Now that we have our own church, the communion of Copts in the Greek church has stopped, because there's no need for it.
So I think the most realistic assessment is to say that our recognition of one another as sharing substantially the same faith is very much affected by local, pastoral circumstances, so it is not possible to generalize based on official statements. Those statements reflect the truth, of course (that we are not in communion), but the reality might be a little different, depending on where you go. This is why many people have pointed favorably to local agreements (such as in the thread on the agreement between EO and OO in Sweden to regular meetings), while at the same time being realistic in recognizing that these do not, in and of themselves, mean that we are reunited or consider each other the same church or anything like that.
Having been to EO churches before (actually long before I had ever been to an OO church; they can be very tough to find, and my home area does not have any, so the local OO go to EO churches...again, pastoral circumstances are so important in how we relate to each other), I can say that personally I see them as being much closer to us than any other communion. Probably if we had a visitor from one of their churches and they didn't say anything, most people wouldn't know based on their practice that they are EO (though of course abouna would not commune them without knowing who they are, and they would presumably know better than to try to be communed anyway). Little variations, like the difference in the sign of the cross, could be noticed, but you'd really have to be looking for them, and honestly nobody is watching a visitor and judging them like that, thank God.
We even have Catholics who come to our liturgies regularly, and they're like family except that they cannot be communed. So on an official level we are still apart, but on an 'unofficial' level, we love everybody and wish that all would be saved, just as we want to be. How could we think otherwise and still pray as we do at the conclusion of every hour? "Have mercy on us, O God, and have mercy on us, who, at all times and in every hour, in heaven and on earth, is worshipped and glorified, Christ our God, the good, the long suffering, the abundant in mercy, and the great in compassion, who loves the righteous and has mercy on the sinners of whom I am chief; who does not wish the death of the sinner but rather that he returns and lives, who calls all to salvation for the promise of the blessings to come..."