The screen is usually the largest consumer of battery on any device, as it takes the most power to run.
Some suggestions I can give about battery drain is to make sure that you are turning off WiFi, Bluetooth, and GPS when you don't need them. They are also large consumers of battery. Apps like twitter, Google+, and Facebook that either check frequently or receive push notifications frequently will also cause drain.
You didn't say you do specifically, but if you use a task killer to stop tasks from running in the background, you are probably causing more harm then good when it comes to conserving battery. This is because even if these apps are "running" in the background, it doesn't mean that they are actually "active". If they are idle, they are not using any battery at all. Killing them causes them to exit incorrectly, and when the device needs information from them, it now has to go through the entire process of starting the application back up. This will use more battery then if the app was just idle and responded to the request that it was asked.
This restarting of the applications that are killed by task killers can also cause the "slowness" you are experiencing. There are a lot of system services that sit idle in the background, if you kill them, the OS may check for these services, as they are registered to be running, and the OS will restart them. This will cause memory to be allocated to restart these services, and the CPU needed to run their initialization processes. Then if you have something like an auto killer, it will see the service starting and the entire process starts again. This basically never frees up the memory these services are using because they are always being restarted. Also the CPU is also always doing the initialization work, and there may be some network communications going on during the start up as well. All of these will cause battery drain, and the device to appear to be running slow.