I think it would depend on how familiar you already are with group exercise principles, how to use the TRX, and TRX terminology. TRX has a specific way of naming and cuing their exercises, and an order of doing their cuing. So, if you want to work at a place that does very formal TRX classes using TRX lingo, then you might want the basic suspension course first.
Just one trainer’s opinion, but I got a lot out of the STC. Since there was no GTC at the time that I took my first TRX certification, I used the skills I learned in the STC to design my TRX group-ex class. Although I’ve never taken the STC, I didn’t need it because I know how to put together a group-ex class. Since then, I’ve been to their training center twice and taken several of the 2-hour sessions at fitness conventions – more than enough reminder education to keep my classes fresh and interesting (I don’t even teach with TRX equipment any more, I use CrossCore, but their training applies to the equipment that I use).