If you plan on getting into tech diving, TDI is the choice. It was the only nitrox course (plus Advanced Nitrox) I offered because you had to do the math.
It goes much deeper into the numbers and you have to think about what you are doing. Depending on the instructor you're likely to get a good deal of extra info.
You could learn proper tank marking because it's a tech diving based class. And you start calculating your own mixes to work for your needs instead of just having to settle for the "standard" mix.
If you are diving the Great Lakes for example, Lake Erie, the mix of choice for many or us was 28%. 32 is too rich and limits your depth.
You'd learn those big ugly bumper stickers that say NITROX on them are not necessary and just a shop money grab.
I learned how to hillbilly blend by topping off a tank with a transfill whip from another and then recalculate the MOD in the tech based nitrox class I took with a NAUI instructor.
You'll learn why it's important to pay attention to the CNS clock, even using recreational mixes, especially on multiday multidive trips.
And there's a good chance that the cost will be about the same.
With the right instructor there could be big differences.