I prefer Anthony Ainley because despite the later panto performances, I always felt with his Master that he was utterly deranged, and he'd do stuff like destroy Logopolis and put the Universe at risk and not realise it, he just put his own greed first. He was an utter psychopath and maybe because of his period in decay, this had made him that way.
I also grew up with Ainley as The Master as as he used to give me the shivers with that chuckle, especially when he was doing it on his first entrance into the story!
Okay, as I said, he did become too pantomime in later stories but he had just that one last chance to redeem himself in Survival and he took it, putting in possibly one of his strongest performances. So glad he was able to have that chance before the show got the axe. The only other thing that I didn't like about his Master was that he didn't use Hypnotism enough, especially during the Davison stories. It wasn't until The Mark Of The Rani that he got back into the habit of using it, but it was a bit late by then, in hindsight.
I do really like Delgado's Master, too, watching him a lot at the moment as I'm going through the Pertwee Years. The only problem I have with his Master is that he too much of a 'Gentleman' Villain, I never felt he had the psychopathic edge Ainley's Master did. Yes, he would kill a Human without a qualm, but he wasn't the lunatic Ainley was. I think of Logopolis when he was just typing evil into that machine in deranged fashion while The Doctor was outside on the telescope, and just can't ever imagine Delgado doing that.
However, he was a brilliant Master in his own right and the first, so like Hartnell and The Doctor, we should be grateful to him for creating the character so brilliant for others to follow.
Should also give credit to Peter Pratt and Geoffrey Beevers who both did wonderfully vocal performances in their respective stories.
Eric Roberts was okay in the TV Movie until the TARDIS Scenes then he went into camp mode.
As for new Who, I totally disagree with above poster who Derek Jacobi wasn't a Master as such. He played the part better in those 5-10 minutes than John Simm ever did in 4 episodes. He was more like The Master than Simm, cold, calculating and evil, just how he should be. Not some laughing maniac who's acts like a big spoilt kid.