I'm current with PADI and SDI/TDI, have been a PSAI instructor in the past but haven't renewed it in years.
If a student insists on a PADI course - sometimes people just can't get past the brand - they get a PADI course, taught to PADI standards (if I'm teaching Open Water, for example, confined water skills are grouped as per PADI's CW sessions). If I'm teaching SDI, they get a course taught to SDI standards. The differences are mostly administrative, diving is diving after all, but they exist. I don't do PADI Tec, so tec courses are always TDI.
By and large, I try to encourage students towards SDI at entry level. If I'm teaching SDI Open Water, I can structure confined water to suit the student - if they have problems with a specific skill, we can move onto something else so they can achieve something positive, then go back and revisit the skill they're finding hard. With PADI, there are a series of brick walls you run into if you adhere strictly to standards, and you can end up having to keep hammering away at the same skill over and over before you can move on. Doesn't happen often, but it does sometimes happen.
Rumour has it PADI do think it's a conflict of interest. I suspect, at least in Asia and the Pacific, that if they do get hard-line about multiple-agency instructors, it's PADI who'll lose numbers.