Strut bars only tie the top of the strut towers together. They will not lower your ride, but they will improve the handling characteristics. You car already has a rear sway bar, the TRD bar is just larger, also improving your handling.
So if you ask me, buy the strut bar first!
If you want to lower your ride, I would suggest TRD lowering springs. This is the inexpensive way. The better way would be coil overs. I just had the springs installed last week and I'm still working out the bugs. Overall, I am pleased with the results.
Hope this helps!
Read through the other threads, lots of info on lowering and handling.