Total Tension Complex? I'm probably not the best to answer (I ran TTC once, I ran Giant ~3 mo). They are very different programs. It is almost like comparing a snatch-only A&A style program to ROP.
TTC is great because the volume is sneaky (I got up to 8, so that's like 63 reps, which is about what some of my Giant sessions were); the TTC is "easier" than the Giant because you don't clean before every press, and for me my shoulders felt more "pumped." The TTC is great because it gets squats in, and it also accounts for snatches and swings. I don't like renegade rows (blech). Part of me wants to criticize the lack of pulling (no clean or row ladders), but part of me also says "bro, you were snatching." TTC is a fun generalist program - you got goals, but they're broad. I want to press more, I want to snatch, I want to swing, and I want to squat - boom, program made for you.
Giant, on the other hand, is laser focused. You will clean and press. It is simple. It is auto-regulated. It is - or can be - very punch the clock. It can also be brutally demanding on your hands - LOTS of cleans! Especially when you're dealing with sets of 10. It allows/accomodates for strength-focus (Giant 3.0), hypertrophy focus (I'd say the first two Giant), and conditioning (the sets of 10 - not saying they aren't hypertrophic). It is phasic. You could just keep cycling through it. But with the laser focus is also the reason I only did 3 months of it - I wanted to do other things too. I wanted to squat. I wanted to pull-ups. I wanted to snatch. I wanted I wanted I wanted. I tried to modify it for a 4th month and it was too much. I'm sure someone better at life could've done it better, but my attempt to modify it failed miserably and I moved on. To be fair I think if I had been more modest with my changes/additions it could be made to work (what could go wrong, C&P for 20 min + Snatches for 20 min?!), but my point more here is the comparison - the Giant is not a Kitchen Sink program, the TTC is designed for it. Start monkeying around at your own risk.
So I don't know how well the Giant and the TTC compare to each other. Both will get you better at pressing. Both will develop the mystical quality called "conditioning." Giant is periodized so you could basically keep using it, the TTC is designed as a one-shot program. If you want or like the simplicity of JUST cleaning and pressing and you don't have a handful of "add-ons" then the Giant is fantastic; if you find yourself thinking "hmm... Only clean and press? Maybe I could add..." Then the TTC might be a better option. Other thing - I think the real benefit of the Giant starts to show in month 2 and month 3 (assuming you run the 1 series and or 2.0).
Hope that helps boss. Maybe @Geoff Neupert
or @John Grahill
(the Giant OG!) could weigh in better, but I didn't want your question to get lost.