There is a Russian and/or a Japanese LHA/LHD that carry more and is faster to boot. Cannot remember the name at the moment. Those darn Russians have the biggest plane, biggest helo and such, you would think they are Texans!
Edit: Pretty sure the one I am thinking about has a capacity of 23K tons.
The only russian one with 23K tons I can remember is AOR-953 Nanyun (Nancang)
(Russia, tech 89, speed 31, range 22224, cargo cap 23K) but that a transport ship not a LHA/LHD.
The japaneese one is probably LHA-18 Chichijima
(Japan, tech 118, speed 62, range 18700, cargo cap 14k tons)
Also, the biggest transport is AOE-1 Sacramento
(USA, tech 63, speed 48, range 18520, cargo cap 33k tons), the fastest (above 10k cargo cap) is TAKR-287 Algol
(USA, tech 73, speed 61, range 25928, cargo cap 25500 tons), the biggest range (above 10k cargo cap) has AO-881 Fuqing
(China, tech 80, speed 35, range 33336, cargo cap 12450 tons)
Don't shoot me if I'm wrong