Well, TGA includes pyrolysis. What you get extra with TGA is that you also measure weight loss (that's the G in TGA) while you are tracking the decomposition process. This gives you a lot of extra information that you can use for composition analysis. For instance, you can look at how the weight changes as a function of temperature and deconvolute the data to see how many discrete reaction steps there are, what temperatures they occur at, etc. TGA has a lot of other uses as well beyond pyrolysis. You can do sorption and water content measurements, oxidation induction experiments, kinetic measurements, and so forth. Most TGAs will allow you to do the heating under several different gases, so you can do combustion measurements, or track decomposition decoupled from oxygen exposure. Basically, it's a more sophisticated instrument. But, if all you want to do is burn the sample and see what the decomposition products are, then TGA may be too much for what you need.
Addendum: I don't know a lot about straight up pyrolysis measurements, but in TGA the sample size is typically very small, 30-50 mg at most. You place the sample in a little pan, which is then hung on a hangwire attached to a balance and then the furnace encloses it. It's incredibly sensitive but not well suited to large samples or samples with highly inhomogenous components. Because it's a sensitive balance, it's not good to have where there will be a lot of vibrations. So, those may be additional reasons a TGA may not be suitable. I couldn't tell you if pyrolysis equipment would be better for these kinds of samples because I've always used TGA for my thermal decomposition measurements. If you're in the market for some of this equipment, I can heartily recommend TA Instruments for any of your thermal analysis needs- they make fantastic equipment and their software is not bad either. We have their DMA, TGA, and DSC in our lab and they make a really nice and powerful set.