They do not.
They want to dig into raids and push hard from normals to heroics. I won't lie, players that prefer 25s enjoy loot like everyone else, but what drives them isn't loot--they do it for prestige. They want to exclaim they beat a 25HM boss because it is a well-known, acknowledged (read: NO GRAY AREA) "most difficult thing in the game" to do. Right now, they can't do that, for multiple reasons:
1. Blizzard continues to pursue to "10/25 as close as possible" agenda: As long as Blizzard defends/continues to design raids so 10s are as close in difficulty as 25s, a 25m raider will never be able to proclaim their dominance as a raider by saying they defeated Boss XYZ. Any 10m raider will simply say: "So what, we beat Boss XYZ in 10m HM and it's 100x harder". Blizzard needs to backpedal on this agenda, and communicate to the players that 10 and 25 can never been equal in difficulty and that they fully acknowledge that 10s are easier. Any further announcements by Blizzard defending 10s in equitable difficulty will continue to muddy the waters surrounding any 25m prestige.
2. There is no Blizzard-approved acknowledgement for 25s: Relying on home-grown algorithms baked by guildox and wowprogress to try to "guesstimate" which guild is further ahead by 25s vs 10s is ludicrous. Blizzard needs to separate the achievements/titles associated with 10/25 raids, and either make it an official part of battle.net site dedicated to organizaing/listing guilds by progress, or update the Battle.net Community API to produce this information in the data dumps so 3rd party ranking sites can order them appropriately.
3. There is no LFR/10 Gate: 25-Man raiders want to push ahead before anyone else, and in a world where a 10 and a 25 can't be fairly balanced in difficulty, nothing disincentivizes a 25m raiding guild more than to put countless hours into a difficult boss, return after a night of wipes, and be greeted with countless guilds that have completed the instance and boast the gear/titles/achievements from LFR and/or 10. LFR and/or 10s need to be gated, similar to how ICC was revealed in 4-week unlocks, so that 25s have an adequate amount of time to push as hard as they need to move from normal to heroic, and even race to realm-first/world-first, without having to worry about the additional pressures of losing quality members to smaller guilds. If a team loses a player because of loot--they never wanted the player in the first place. With this structure, a 25m guild will be *unable* to lose a player to a smaller guild/LFR for prestige...it simply won't be an option for those brackets of raiders.
You'll notice in my suggestions I never once touched on changing the loot/rewards. I, as a 25m raider, felt very strongly that 25m deserved the reward of better gear and loot as an acknowledgment for the effort that goes into a 25. However, I've always been a proponent of the idea that everyone deserves a chance at experiencing the game (READ: chance to experience IS NOT THE SAME AS entitled to loot), and loot goes along with this. Not everyone can (or wants to) raid 25s, but they *do* subscribe and they *do* deserve a chance to earn those rewards. So, in order to re-incentivize 25s without touching loot--the above points need to be addressed.
1. Blizzard, make an announcement/take an official stance on "LFR is easy, 10s are medium, 25s are hard", and design for that.
2. Separate the LFR/10/25 Achievements, and produce LFR/10/25 unique titles and or mounts as rewards. Don't touch loot; leave as is (the upgrading was actually kind of cool).
3. Open the full raid on release for 25s, gate LFR by iLvL, and gate 10s by month-by-month unlock, a la ICC.
I don't know that this will solve ALL of the 25m raiding incentive problems, but it will get you closer than "just having 25s drop more loot", while at the same time, not take anything away from LFRs or 10s.