If I may ask, are you planning on playing moderate to heavy games and using work-heavy applications like video editing or other adobe applications?
Or are you merely browsing the internet and watching youtube/netflix while playing light games like minecraft?
If your answer gears towards the second one, I recommend not upgrading your motherboard and saving your money until you can upgrade your entire system for a more modern cpu/ram/motherboard.
It makes very little sense to upgrade your motherboard if your cpu will no longer fit the socket and if your ram will no longer work. Unfortunately, once you change the motherboard, your ram and cpu will most likely no longer be compatible.
So, all in all, if you would like to do more intensive work on your computer, yes, I recommend switching, but only if you're ready to buy the motherboard-cpu-ram combo all at once. Otherwise, or if you're only browsing/microsoft word and stuff, I recommend staying on DDR2 and saving your money.
Edit: For the record, it's not the change from DDR2 to DDR3 itself that improves performance drastically, it's the implication that you're improving your CPU and motherboard and perhaps graphics card also that tends to drive that correlation of improvement.