The fire rated doors are usually made of some kind of mineral core material and they are usually more dense and therefore do usually add a few more STC points to the door. Usually.
There are a few charts comparing the STC rating of doors with different cores from various manufacturers. Here is one of them and I am sure you can find more. http://www.masonite.com/pdf/accousticalData/AcousticalPerformanceInterior.pdf
But, generally speaking a solid core interior door is in the STC 28-35 neighborhood with the mineral core usually near the top. On the other hand there are some non fire rated doors showing a 33 rating. Be careful about how the tests were performed. Sometimes they test doors with different types of seals which will make a huge difference as the seal will be the weakest point.
If your room was done with sound isolation techniques then you should do all you can with the door to stop the sound. If it was not, then you will probably see minimal benefit as there are many other flanking paths the sound is taking to make it to the rest of your house. You never know till you try of course but I am just passing along the information given to me.
Links to other threads on avshttp://www.avsforum.com/t/1420022/door-to-prevent-sound-tranmissionhttp://www.avsforum.com/t/1294101/sound-resistant-doors/30http://www.avsforum.com/t/1179332/what-type-of-door-should-i-get-for-good-sound-proofing
Here is a link to a door SIM from thesoundproofingcompanyhttp://www.soundproofingcompany.com/soundproofing-installation-manuals/sim-doors/
If you want to know even more there are more helpful links in my build thread thanks to other folks trying to help me out.