I've been playing this game a while, and generally end up in solo queue.
I'd like to play ranked, but don't want to risk creating problems for my team due to errors.
I'd say that I'm a pretty solid player in general, and know all the theory, but I have a few weak points.

The thing is, I have an excellent record on Twisted Treeline, but when I play on Summoner's Rift, my win ratio is much poorer.

I know that the first is a microcosm of the second, and in theory the only real difference is jungling on SR is done by a single dedicated player per team, while on TT it's much more haphazard.
As well, there is much less laning involved, although it still plays out to some degree.

I'm wondering what other major differences there are.
Things I've noticed:
Map control: Check. Getting red buffs and dragon kills makes a big difference.
Creep kills: Check. Not as big of a deal, but still important.
1v1, 2v2, 2v1, etc. Check. Not as many combinations as 5v5, but when you're outclassed, you run away regardless.
Pushing towers: Check. Perhaps not as important as in SR, but still relevant.
Capitalizing on opponents death: Check. On both maps, when you have a team advantage, you want to push an objective, be it dragon or a turret.
Map awareness: Check (although to a lesser degree). Mia is still important, warding/checking bushes relevant, etc.

Can anyone who has played both extensively point out areas to develop more to get better on SR?

You just need time to adjust to the map and the common play styles in SR as opposed to the ones in TT. Things like how far you can push, where you are generally safer, where is good to ward etc are all things you can learn best with practice.

I'd advise playing some blind pick games until you start to get some more confidence. I used to play TT all the time and made the transition just by keeping at it.

Someone wrote a good guide a while back and unfortunately I can't remember where I saw it, but one of the things it said that stuck out to me the most was that 5 people can put out a lot (and they emphasized A LOT) more damage than 3 people can. I don't know if that helps but it's something I never forgot. :P

Also wards. If they have a jungler make sure you get them as soon as you can and put it somewhere that will give you a heads up if you're pushing. Junglers like to be unpredictable and will come from (using bottom corner as an example) the tri bush path, the river opening or the path near blue tower. Most of those are effectively countered by placing a ward either in the bush where the river meets bottom lane, or a little further up so you can get more time to get back.