Argh, I accidentally lost my long reply to this, so I'll try to be somewhat more brief.
Your framerate is directly proportionate to the amount of computing power you can throw at rendering a scene. So the faster a CPU, RAM and video card you have, and the more system memory and video memory you have, the faster you can render a scene.
As well, the less data there is for your computer to render, the faster it will do so. So now, when you say that you get 35 FPS in a certain sim, that's not really what's happening. It's not tied to the sim, it's tied to what your camera can see. Try for yourself. Hold down Alt and click and drag in and out on the ground. Watch your framerate go up and down as more objects come into view. It's more that certain SPOTS in certain sims are laggy, because they have a large number of textures and objects.
Your connection speed is the time it takes for a single packet of data to reach its destination. Bandwidth is capacity -- how MUCH data can you transfer? As I said before, the two are not one and the same. Compare it to snail-mail. If I want to send a letter to another country, I can affix my stamps, and be reasonably well-assured that it will reach its destination in a week or so. OR, I could have it sent via FedEx, and get it there first thing the next morning. The same amount of data is being transferred, the difference is just in the speed it takes to get it there.
A shipping crate full of hard drives filled with data is a very high-capacity "transmission" method, but it's very slow. A telephone may be very low-capacity, but it's (relatively) very fast. Depending on the distances involved and the amount of data required, either may be a viable solution for transmitting data.
Because SL needs both capacity (for streaming content like objects and textures) and speed, (for keeping things updated and so that when you push 'forward', your avatar actually responds) the best connections are ones that are both high-speed and high-bandwidth. Dial-up connections are out, because while their speed might be sufficient, if a little on the high side, their capacity is a FRACTION of what's required. For most practical purposes, a satellite connection is out, because while it's very high-capacity, the actual SPEED you're likely to get really isn't that hot at all. It tends to be anywhere from around 10 to 30 times SLOWER than a modem connection.
So your experience in SL is shaped by a number of factors:
1. Your framerate and QUALITY of rendered images.
2. Your connection speed and bandwidth.
3. The amount of data required to download.
4. The sim's performance. (Affected by things like number of concurrent users, number of physical objects in the sim, number of scripts, etc.)
Basically, by upgrading your video card, you've VASTLY increased the quality of SL's appearence, and (I assume) marginally increased your framerate. Everything else remains the same, and so, will not improve.
Edit: finished what I was saying.
