Cheeseandpepper,
:welcome: to DroidForums.net! It's a shame that your first post has to be about the piss poor battery life you are getting now.
Getting three to four hours of battery life is unacceptable for light to average use. The twenty hours you was getting with your old phone is more consistent with your usage. I guess we just need to pinpoint what is sucking the life from your Droid.
There are a number of things that could be going on here, but regardless of whether you are rooted or not the first step should be to determine if you have an app installed that is constantly eating up CPU cycles.
Look under Settings > About Phone > Battery Use. Does anything there stand out as an obvious culprit? If not then you might want to download an app from the market that is capable of showing you in real time all services and applications that are running and the CPU load they are using.
If you don't know of any good apps to use, OSMonitor will work just fine. After installing it, open it up and look on the default tab it shows. Here will be a list of all running processes and on the right will be a percentage. This % indicates how often the process is using the CPU. If you notice any process in that list that is repeatedly registering a high percentage then pay special attention to the process name.
If you can find an app eating up your battery this way, good. All you need to do is uninstall the problem application and hopefully this will improve things.
If not, then let me know so we can move on to what to do next. Also let me know if you are rooted or not, as that will help a lot in my next advice.
By the way, the other night I noticed that my battery life was horrible as well. I'm rooted, overclocked, and running a custom ROM so it took me a little longer to fix the problem but I eventually found it. I use SetCPU to help with overclocking and I realized like an idiot that I had set the governor to Performance, meaning that even when my phone was asleep it was running constantly at 1.2Ghz. Normally I get around 8-9 hours of pretty heavy usage but this had sucked my battery dry right fast.
