If there were no differences between agencies, then why are there more than one? The whole "it's the instructor, not the agency" is just scuba board political correctness - that provides instructors an avenue to feel good about themselves when they commiserate about how they had to correct deficiencies in another instructor's student from their same agency!
If you really care about this topic, research the history. Ask yourself how padi came to offer, in this case, technical training. Did they design it? Or did they bad mouth technical for decades, and then when they thought they were missing out on business - did they hire an IT from another agency to share the other agency's program with them - and then customize the other agency's program to padi's rigid training method?
Then compare and contrast that to, in this case, tdi. what is tdi's history? does it predate that of padi's in technical? Does tdi's ideology on gas choices, buddies, and ethics, etc. match yours?
When you finish your training, and actually want go out to dive at that level - and are looking for buddies, or operators to take you to sites for that level - do you think either certification will be equally respected and allow you to immediately dive at that level? Try calling operators / guides / etc. and ask which training programs they are more likely to accept for advanced dives sight unseen - I would be interested in the responses.
May I ask why you are choosing to limit your technical training to only padi or tdi?