A stable 10 man has 2, maybe 3 people on the bench. A stable 25 man has about 10 people on the bench because there's a far bigger chance of someone having to be absent in a 25 man than there is in a 10 man, not to mention the fact that setups are far more important in 25 than 10, meaning you NEED that many people.
12/2 (12 people, 2 pieces of loot)= 1 piece per 6 people.
36/6 (36 people, 6 pieces of loot)= 1 piece per 6 people.
That's about as simple as I can put it.
Either way, you can put out as much anecdotal evidence as you want - in the end, I really couldn't care less. I lead a healthy top 50 guild, and I have tons of friends in both raid sizes. I know my numbers are pretty accurate, on average (there's outliers in both sizes and on both ends of the spectrum).
As for the Ilvl difference,
Recorded Guild Item Level: 566.65 (25-man) <-- Method.
Recorded Guild Item Level: 565.66 (10-man) <--- Paragon.
It's pretty close - but that aside, Method did far more for their item level advantage than Paragon did. I mean, 8x 25 man runs the first week as Aladya claimed previously - if I recall correct, Paragon did 3 runs, but that could be wrong (if anyone has the correct number, feel free to say so).
I'm also not aware if Paragon did the same as Method did during heroic modes - Method would kill a boss on heroic, then take the mains that were left out for the boss kill, and kill it again on normal to maximize loot. As Paragon kept a 10 (11?) man roster, that would neither have been productive nor worth it, I guess - which means that you effectively have so many more raids worth of loot for Method because of the way they played.
That bosses are as setup-dependant in 10 man as they are in 25 - they're not, so you're going to need a larger bench in 25 purely due to setup issues (Thok heroic was 8 healed during progress, siegecrafter was 4 healed, in 25 man. In 10 man, that was 3/2 healers. Usually you have a designated hybrid to switch between dps/heal for 10 man heroic guilds to keep the team even tighter, but I'll concede that this could be a bench spot as the same COULD be done for 25. So, just because of healing setups, 25 man had to have 3 more people on the bench to get through the tier).
That the amount of absenses and attendance issues will be the same between 10 and 25. If you have one person absent in a 10 man from a raid, that's one person you need on the bench - but in 25 man, you're just as likely to have 2.5 (3) players absent as a 10 man is to have one player absent. It's basic math. You need more people on the bench to be able to fill in for absent people, because there's more people to be absent.