*cue the Queen's voice from Mirror Mirror* There's no such thing. Anythony Andrews couldn't have outdone Rex Harrison's Higgins because that's simply humanly impossible.
I missed the broadcast of A.A.'s MFL, but I have listened to a bit of Andrews' performance, and...I remain as staunch in my belief as ever. Remind me exactly why we prefer his portrayal to Rex Harrison's?
While I'm sure Anthony Andrews was delightful as Higgins (I personally didn't enjoy what I heard that much, but...as you've noticed, I'm somewhat biased:D), Rex Harrison, to me at least, took Higgins and basically embodied him. He IS 'Enry 'Iggins to me, a confirmed old bachelor, and quite likely to remain so;)
This isn't to say I don't think Mr. Andrews is a remarkable actor. He is indeed (TSP and the little bits of Ivanhoe I've seen). In fact I'd love to see more of his work. But I felt that I had to defend Mr. Harrison's *coughcough* Academy Award-winning performance *aHERM*.