Gay marriage not recognized, gay civil union is, but only in certain locations in the country at the moment. Hopefully this will change soon.
Civil union essentially awards you the rights to claim a partner as a dependent, take out health insurance together, and really I don't know what else, especially since right now it is only recognised in a few places around the country -- ie you're recognised inside Capital but travel outside the General Paz and I don't know that you are.
Since it is not a federally recognised status, civil unions performed in Argentina are not recognised in most other countries either, so if you want to have a civil union and then emigrate to another country you have to bring your partner in under the conjugal not spousal category, if that is possible in the country where you are emigrating to. And for proof of conjugal status you will essentially need a binder a few inches thick full of photos, receipts of trips you've taken together, rental agreements with both your signatures on them, utility bills in common, testaments from family and friends (I kid you not, my best friend is going through this right now to bring his Argentine partner, with whom he has an Argentine civil union, to Canada -- fortunately these days most hotels send receipts via email so he has good evidence of their holidays etc -- if only they had just married in Quebec then they wouldn't have to be amassing all of this info).
Furthermore, unless they have changed the ruling once again, when you get a civil union here you have to have proof that you have been a couple for at least 2 years. I'm not sure if they ask for specific documentation, or if it is an interview, or what. You need, as for a marriage, at least 2 witnesses. In the registro civil notes it says that you can have up to four but that at least 2 need to be residents of Capital -- this seems ludicrous to me in this day an age, like a rule that must have been written in the 1800s, but maybe it's true, although I really have to doubt that.
Now, as far as gay couples who have been legitimately married in say, Canada or South Africa where it is fully legal, and who choose to move to Argentina, I am not sure how they are recognised by the government or migraciones, or if their marriage is considered invalid when they return. I'd be curious to know -- if Argentine civil unions aren't recognised abroad, are gay marriages performed abroad in countries where it is legal recognised by Argentina?