At my first competition, Lyon Open 2007, I did a lot worse than I was at home (my at-home avg was 16-17, my official avg 19.99/19.47)
But at my second competition, Italian Open 2008, I did really well. My 3x3 avgs were normal or even a bit better than average averages for me at that time (except for the finals, but that's a different story

).
My 4x4 times were as at home and my 5x5 times were a bit better than at home. I even set up my single PB for 5x5.
My Magic times were a bit worse than at home (ok, I hadn't practised for a long time), and my OH times were good.
The Megaminx time was very good for me
Just the 2x2 was not that good, but still ok.
So my overall performance was normal.