Though I'm no expert on the subject, I believe that the Syrian Orthodox church (OO) and the Assyrian Church of the East (Nestorian) were a number of years ago close to reunion. If my memory serves me correctly, an editor at socdigest.org said progress in the reunion of these two churches came to an end by the influence of Pope Shenouda III. I have no desire to upset any Copt or OO Christian on this site, this is from a conversation I had with the said editor using IM about 2 years ago. If I'm mistaken, I'll gladly be corrected.
p.s. However, looking at socdigest.org, the authors often seem to have strong ties with the history of the Assyrians in the Far East, almost speaking of the Syrian Orthodox Church and the Assyrian Church of the East as one church.
If that's the case, then I wish to get a Syrian Orthodox perspective. I personally am speaking from a Coptic perspective. But you're not upsetting me or anything. I think the fact that some Syrians actually wanted to unite with them is something we should address and not keep hidden, which is something I seem to see is being happened.
As far as the Coptic Church is concerned, we criticize them for believing in two hypostases and two prosopa. According to an alleged conversation between HE Metropolitan Bishoy (HEMB) and an Assyrian bishop, which according to HEMB was recorded, the Assyrian bishop gave the analogy that just as we believe in one incarnate nature as the same as of two natures, so they believe in one person of two persons, to which HEMB replied, "Then you still believe in the continual reality that two persons exist."
I understand this is quite a simplistic way of putting things, and I may understand that the appellation "two persons" might mean something else (in the OO tradition, we also are pretty close in saying "two hypostases", but never "two persons"). Like I said, I never had a conversation with them, and I never did heavy duty research to have my own opinion of them. One thing I'd like to see addressed is the charge of "Nestorian Monotheletism" made against them by Fr. John Romanides.