A good tech instructor will always teach you what you need to know, irregardless of agency. PADI normally produce good materials, but the tech 40/45/50 manual is a shambles at the moment. It hasn't been updated since the program chanced from the old 'Tech Deep' system. You get a wad of supplements instead...and different knowledge reviews from those in the manual. In isolation (one course/module only) this can cause confusion. However, when applied to the entire Tec40-50 syllabus, it's still a very comprehensive resource. Shame the pictures weren't so "PADI-fied" though...
The TDI manuals are basically just supplements anyway...wire-bound with a plastic cover. I think they (and the IANTD) work very well if you're only interested in an isolated course. There's not as much continuity as the PADI manual has. That's a good thing, or a bad thing, depending on your training plan/goal.
In respect of the courses, the biggest difference between PADI and the rest is at the entry-level. The Tec40 is a more rounded introduction to technical diving, wheras (IMHO) Advanced Nitrox is more specific and needs elements from deco procedures to complete it. Tec45 continues Tec40, with more detailed dive planning and greater deco. The Tec40 teaches quite a lot, but the recommended standards keep you at baby steps. The Tec50 - Extended Range level is virtually identical between all agencies - deep air down to ~50m with a wide range of deco options.
There's little to nil difference between agencies when it comes to recognition or acceptance. Tech is about the diver's actual experience and ability...with maybe some credit for the reputation or 'name' of their instructor. The plastic card itself counts for very little, I've found.