I don't have any physical issues that drove my decision to buy a FS bike, but yes, it is a nicer ride. That said, do you have back pain in general or are you having discomfort riding your new bike? If it's the latter, it could be that the fit or set up is off. Make an appointment with a fitter to see if there are things you can do to help. Or, if you're new to biking, it could be a matter of building some additional fitness and core strength--keeping in mind that you may have to work on building that fitness both on and off the bike.

Whether you're on a FS bike or a HT, it's important to remember that your own body is part of your suspension. Especially if you get out of the saddle for obstacles, you can make better use of your arms and legs to help absorb shocks.