From lots (and lots, and lots) of experience in Acts 1 and 2 Inferno, I do not believe Elites and Champions gain any extra stats beyond health from being an Elite or Champion. There are abilities that increase various attributes (Fast, Extra Health, etc.), but Elites and Champions don't hit harder or move faster just because they're above average.
When a monster is attacking you (ie. using their default attacks, not something conferred by an ability), I have not noticed any of them hitting harder or moving faster than their normal counterparts.
The difficulty from these monsters comes from the special abilities and AI modifications conferred by being above average. As far as I have been able to determine, abilities that directly cause damage (Arcane Enchanted, Fire Chains, Molten, etc.) don't base their damage off the monster type; it comes from their level. ie. All Molten fire patches in Act 1 Inferno will do the same amount of damage, regardless of which monster is generating them. This is because all monsters in Act 1 Inferno are level 61. Molten monsters will also often try to walk around you, to make sure you're standing in their fire.
Unique monsters are slightly different; they have special names and the same abilities and monster model, regardless of when you meet them. These monsters have their own set parameters that they will spawn with.
When a monster is initially spawned, you can notice that some randomization is going on, just by looking at their health values. This same randomization would apply to above average monsters (including Uniques), after which their special abilities would be calculated and finalized.
I have no official source or methodical testing to base this off of; it all comes from my observations when fighting groups of monsters.