Lets see, Would upgrading be a good idea... yes, necessary... no. Let me explain.
As of right now, a majority of the programs and systems still use a 32 bit operating system. The general population is ever so slowly being moved from 32 bit to 64 bit. The drawbacks of 32 bit is precisely what you mentioned, the RAM. if you use a program that uses a LOT of ram, or could utilize a lot of ram, then 64 bit is the way to go. If you do not, then 32 bit will work perfectly.
Eventually, the entire general public will be completely moved over to 64 bit, and although 32 bit wont disappear for a while, it will slowly begin to fade out just as things like Windows 2k and Windows Me did. How soon or fast, is really decided on how accessible and obtainable the new software is.
By upgrading to a 64 bit operating system, you are guaranteed to be able to install and run any software that will come out (granted it isnt a specialty item). At the same time, you will be able to use any 32 bit softwares that come out too (or that already exist) because a 64 bit system CAN run a 32 bit piece of software. I currently run Win7 64 bit, and if i were looking at purchasing a new OS and money wasnt a factor, id go for 64 bit. If money is a large factor, and you already have 32 bit, then just stick with 32 bit. You wont need to upgrade for a bit longer.
All in all, the simple difference is just as i stated before, memory. Thats the main additional function of the 64 bit operating system. 64 bit operating systems can utilize more RAM and more memory more efficiently than could 32 bit operating systems.
Hope this helps, i did my best to keep it simple. Let me know if you have any more questions and ill do what i can to answer them.