Questions like this are interesting, which is why they're often bait on message boards. Good to see this conversation is civil.
Online Orthodox tend to be converts who read their way in through studying theology so of course in places like this you'll get a strong repetition of Orthodoxy's one-true-church claim. Catholicism claims to be the one true church too.
On paper, Orthodoxy's one-true-church claim is narrower than Catholicism's. The Catholic Church sees the Orthodox as an estranged part of itself. All Orthodox defined doctrine is true (to Catholicism, Orthodoxy's Catholicism written in 11th-century Greek terms); the Orthodox have real bishops and a real Mass. So sacramentally corporate union is possible (the clergy would be received as clergy, the way the Eastern Catholic churches were started), and as domNoah wrote, individual conversion is much easier than bringing in an ex-Protestant. I think all you have to do is make a profession of faith witnessed by the Catholic priest. Make your confession if you need to, make your Communion in the Catholic Church and, if you were a born Orthodox or an Orthodox convert who was not a born Latin Catholic, you're an Eastern Catholic, officially belonging to the Eastern Catholic church corresponding to the Orthodox one you came from (so Antiochian Orthodox would become Melkite, etc.).
The Orthodox on paper have no doctrine mirroring Rome's recognition of their orders and sacraments so you get a wide range of opinion. In practice they often do mirror Rome's recognition (so an ex-Eastern Catholic wouldn't be received by chrismation, ex-Catholic priests are received in their orders, etc.). But not always. There are strict jurisdictions that receive all converts, including Christians such as ex-Catholics, by baptism. Because the only Orthodox doctrine about this is 'Orthodox sacraments have grace'; the rest is a big unknown. So to such hardliners (monks on Mount Athos and many online converts, for example), an Eastern Catholic church is like a Protestant church such as the Episcopalians putting on an Eastern liturgy: no real priesthood, no guaranteed real presence of Christ. So they see an Orthodox becoming an Eastern Catholic as just like becoming a Protestant.
In 20+ years of knowing Eastern Christians I've only met one born Orthodox who switched, for probably the reason most of the few who switch either way do: he married an Eastern Catholic.
In the churches' ethnic bases in America you now see almost no movement back and forth. The ethnic born Eastern Catholics don't identify with the Orthodox at all. It's basically Latin Catholicism with a modified Eastern liturgy. I'm thinking mostly of Slavs: Ukrainians (the biggest Eastern Catholic church) and Ruthenians.
Then there are the Melkites here and in their homelands, Syria and Lebanon. In practice, never mind the one-true-church claims. There the Melkite and Antiochian Orthodox laity are functionally one church: they intermarry (the wife always joins her husband's church, no questions asked), intercommune and are baptized and chrismated at each other's churches. The only division is the clergy don't concelebrate. So many Arab immigrant Melkites are technically born Orthodox and vice versa.
So enough about theory and high-flying theology. Practically for you it probably wouldn't be a big deal, depending on your background. Again to Arab Christians, no big deal. Greeks, Russians and convert Antiochians? A big deal.
One can agree intellectually with 100% of Orthodox doctrine and still be out of communion with the Orthodox Church.
Right. You have 'outliers' in the Orthodox communion such as the Old Calendarist churches (in which I understand one of our hosts is a priest) and the Russian Old Believers, technically not in the Orthodox communion but 'still in the family'. In practice they're almost always recognized (received into the official church in their orders, etc.). You have occasional phenomena like the Evangelical Orthodox Church, the faction that didn't join Antioch, essentially Protestants who are self-ordained and believe in everything Orthodox yet stay out for some reason.
Likewise among Eastern Catholics you have the extremely rare phenomenon of 'Orthodox in communion with Rome', almost always converts/born Roman Riters who switched. Not to be confused with the converts who try to do exactly what Rome tells Eastern Catholics: be just like the Orthodox liturgically. The OicwRs follow Rome on that but side with Orthodox opinion against post-schism Roman defined doctrine, which doesn't make sense. Usually they end up just passing through; they get fed up and become Orthodox.
My parish priest does not teach the immaculate conception, He says theosis is a process last lasts eternally after bodily death and as far as I know has never said anything about purgatory, the Filioque has been eliminated from the creed.
There are Eastern Catholics who do what Rome tells them — express Catholicism in Orthodox terms, which this might be. (For example: Mary is all-holy/sinless but if you're using Byzantine theology to describe original sin, you don't need the Latin description of the Immaculate Conception. Not really denying the IC.) Then there are the OicwRs.
So as I read it, this hypothetical person isn't a free agent who is debating between joining Orthodoxy and joining Catholicism; but rather someone already in Orthodoxy and thinking about leaving it for Catholicism. In that case I think the most relevant text is Balamand: "Pastoral activity in the Catholic Church, Latin as well as Eastern, no longer aims at having the faithful of one Church pass over to the other; that is to say, it no longer aims at proselytizing among the Orthodox."
This needs explaining. Catholicism's big goal isn't individual conversions but to bring in the Orthodox intact. But, because, like the Orthodox, Catholicism claims to be the true church, of course it still accepts individual conversions; it just doesn't solicit
never-Catholic Orthodox to individually switch. (The Eastern Catholic churches are mostly attempts to convert the Orthodox that largely failed for various reasons, including Russian expansion and persecution.) It accepts them, but quietly
According to its doctrine, the Catholic Church doesn't tell you to hate the Orthodox tradition, which is why in part the Eastern Catholic churches exist. They often fall far short of the goal, but they're supposed to show that regard for that tradition: how those churches should work under Rome.