Unfortunately I wouldn't hold my breath for those improvements to happen.
very few sites (if any, really) are PS3 browser optimised, and Sony goes pale at the thought of unsigned code running on their systems so until they sort that out it's business as usual I'm afraid.
I'd love to see FF on PS3, but due to the more "open" nature of Mozilla and plug-ins, I can't see it happening.
occasionally though Sony does improve versions of flash player and codecs like those from DivX but those are few and far between.
Personally, I have no trouble with either gmail or online windows live mails myself but have had problems with VGChartz and other random sites, also the slowness.Youtube works fine though from what I've tried so far (haven't used it for a while)
*tinfoil-hat-time*
as PSN is also quite slow in comparison to other console online services, I have a sneaking suspicion that that the PS3 sends everything through a proxy of sorts on the Sony side, be it for web browsing or PSN. although remote play with PSP's is pretty zippy from my experience so I don't know. maybe just some types of traffic get routed through the Sony proxies or something.
*takes off tinfoil hat*
all that is just suspicion though and probably wrong, but its something that's been bugging me for a while.
Could also just be the way PS3 handles the TCP/IP stack (i.e. badly)