Some of you have way more experience than I but I'd really lean towards some light tech before becoming a DM assuming you'd be leading dives where the extra theory knowledge would come into play. I like the theory portion, sure you can read books but actually getting in the water and seeing what happens makes the difference for me.
Leading dives, what computers are absurdly conservative, this guy is diving GF 95/95, this person forgot to reset the gas they're breathing and has 15 minutes of deco - I like knowing more about things than what was provided in the DM class.
Again - I guess it may come down to what are your duties as a DM, if you'll mostly be assisting instructors, maybe a firm understanding of advanced theory isn't what you need. Tech diving cleaned up my diving, much more thinking goes into falling in the water on every dive, not just planned deco dives.