Lots of good feedback, and some good points being made. Thanks all.
As ever you can make it fit any organisation you like if you stretch the definition as you wish. On a level playing field (to mix metaphors) a lot of organisations that - on paper and in PR - look like they're well into double figures actually don't field that much in reality.
Here's some suggestions to what I think is reasonable criteria to use. It's not proving anyone's better than anyone else or that some things don't count, just trying to make a consistent measure for the purpose of the discussion.
It's Gotta be heavyFor this debate I'd eliminate dedicated trainers and L birds. Important though they are, and genuine warbirds, I think most of us would be looking for the interesting counts to be fighter and bomber orientated, and a L-bird-only or trainer-only collection, while perhaps bigger wouldn't be the 'right' answer. I'd suggest trainer versions of fighter and bomber types are in, such as Spitfire T.9 or Vampire T.11s, while Tweets don't count, A-37s do.
Defining a 'warbird'Again, up for debate. I'm suggesting, for the purposes of this discussion W.W.II era to Vietnam types. So earlier (however much combat) aircraft don't count. Post Vietnam likewise, because they are pretty rare and the maintenance / opportunity criteria are completely different.
OriginalityFor this discussion, it doesn't matter, as long as it's the original structure type and engine type, or near. So wooden Spitfires with non-RR engines are out, Flug Werke FW 190s in.
Extra points for enginesWe'd all agree that a B-17 is a bigger deal to operate than a Mustang, and a Lancaster or B-24 more demanding than a B-17 due to rarity of parts etc. We could count cylinders and have a handicap system for rare types, but that'd be getting silly (whereas this is all very , very sensible, isn't it kids...) Let's say multi engine and rarity counts for tiebreaks. Are jets tougher or easier?
Gotta be publicAnd that means more than one event per year involving the 'whole' organisation. Again for tiebreak purposes, multiple roadshow events get extra points, particularly away from base.
REALLY Current"Tomorrow we'll have" and "Airworthy but hasn't flown in the last five years" just doesn't cut it. Airworthy flies, sugar walks.

It's all important, and in no way to degenerate those restoring aircraft or missing the effort a restoration section costs in effort, but this is about current, active fliers, not 'airworthy but never flown' or 'next year'.
And heritage counts, but not hereThe redoubtable Collings Foundation roadshow have a lot more places to get to to touch the Battle of Britain Memorial Flight's fifty plus years and now more than 700 individual aircraft appearances per annum. But we are just looking at right now, not how long you are doing it. Likewise taking people aboard gets extra points I'm sure we'd agree.
One CollectionAnother tricky one. Either owned by.. or loaned to.. I'd suggest are reasonable to include, not just 'hang(ar)ing around'!
Anyone wants to debate the definitions, you are welcome - but for the purposes of this question (mine) it's my definitions, thanks, start your own thread for the 'what's a warbird' argument.

For the purposes of the discussion, feel free to make exceptions to mention an organisation, but be warned - if you don't mention the change of the rules, I will....
It's just a bit of fun so keep your thoughts coming, but let's try to run the same ruler over each contender. (And they are all valued, I'm sure we'd all agree.)
Cheers,