Heres my two cents..... I am a long time PADI instructor, did DSAT up to Trimix a few times (I sat in), and just became an IANTD Adv. Rec Trimix Instructor, and just did my first rebreather cert with IANTD. So I have recent experience as a student and instructor... Here are some general observations, this is just my opinion based on my experiences.
IANTD... the materials vary. that is they have tons of good info, but no organization at all. Much of it very hard reading, technical essays and theory. tests and books and answer keys dont match up, all in different stages of development. Some info too vague, other info too in depth. IANTD says this will all be worked out this year. Presentation slides are good. Required water skills are good too, and the grading system/peformance requirements are great. But skills are not previewed in a video or in the book, not well integrated at all. A good instructor is key here.
They are really big on rebreathers, so a good choice if youre going that direction. Smaller agency, but the original tec agency, so pretty well known. Go to ProTec in Playa, they have a great reputation, Id train with Matt any day.
TDI- dont really know much about them. Advanced nitrox manual is exactly like PADI nitrox (but higher o2 limit), so pretty good. My boss is a IANTD and TDI IT, doesnt teach TDI due to problems with getting certs processed. I never finished the Adv nitrox class, cause the instructor (different shop) was terrible in the water, on the other hand the best oc diver I know is TDI (and GUE).
A good instructor is important here.
They are (were?) the biggest tech agency, especially in asia, so for working it might be a good idea.
DSAT-materials are awesome of course, but a little over simplified and goofy. The deco/gas planning section is the best ive seen. Skills well integrated with academics, and previewed in a movie. But they fall down on required skills and performance requirements. Finning has been addressed by others here, its a serious oversight. Skills are not broken down for students or instructors (unlike in PADI DM programs) anywhere that Ive seen. You can get an excellent DSAT class, but a good instructor is especially key here, and that usually means they teach for another agency too, with better skills requirements that they will incorporate (the whole finning thing again) into the course. I think the minimum skills requirements have the potential for turning out incomplete tech divers, who may become incomplete instructors. The agency is looked down on by much of the tech community (a lot of that is political), but it will soon be the largest one.
All the agencies have different philosopies on equipment, gasses for deco, etc...you should research this and find one that suits you. The most important thing is what they all have in common, and that is you have to have a good instructor.
This is all just my opinion based on my recent experiences. Others will have had different experiences. I dont know about other agencies, and wont speculate, other than to say GUE will have the best skills, and fundies will make you a better diver, regardless of what agency you do tech with.