My answer to this is a historical anecdote, but the quite informative answers here do talk about what happened in the 1990s, as well as what’s happening now.
The reports now are that Albanians are on the top of the totem pole of immigrant privilege. They are of course still below Western Europeans, who are treated as a separate category entirely—though I’m not sure if Greek goes as far as English, to have a separate word like ‘expat’ for them. Albanians now are well-regarded, as householders (νοικοκύρηδες) and small-businesspeople, even if they are still often regarded as the hired help rather than equal members of society.
I’ll add an anecdote from 1995 that left me puzzled.
I was in Greece for six months, doing archival research for my PhD, and staying with relatives. At the end of the first three months, I had to go to the local immigrant processing centre, to renew my visa. (I am an Australian citizen.)
The courtyard of the centre was chock-a-block full of Albanians, waiting to be processed for the holidays. None of them was being processed, and noone was going inside. I am Australian, so I believe in queues; so I hung about for maybe an hour, trying to listen in on the Albanian all around me. (From linguistic research, I knew a bit, though certainly not enough for listening in to work.)
After a while, one of the Albanians turned to me and said (in flawless Greek):
—You’re not Albanian, are you.
—… No, actually, I’m not.
—Well what are you waiting with us for? Go to the front.
… I guiltily skulked to the front. The doorman said:
—You’re not Albanian, are you.
—… No, actually, I’m not.
—Well what are you waiting with them for? Go inside.
Thinking back, it may well have been that there was no queue, and there was a designated Albanian processing time. Still, the fact that Albanians themselves pushed me to the front of the queue was something I found chilling.