I agree TDI Nitrox will be head and shoulders over PADI Nitrox in terms of depth of material covered.
However having taken both TDI and IANTD trimix courses, my feeling is that IANTD offers much more thorough courses with higher in water standards and a larger number of skills that are taught and assessed.
That said, it also comes down to the instructor and what he or she adds to the course. I have also noted that some TDI instructors will augment the course with some IANTD materials and many instructors (the good ones) regardless of agency affiliation will (and I think should) teach beyond the minimum standards and expect more than just minimum performance.
I am pretty biased given a technical diving back ground, but as a diver originlly certed by PADI in 1985, my impression is that PADI started seriously dumbing down the OW and AOW courses in the late 1980's and 1990's to make diving more accessible to a much larger potential market to support what has primarily become a travel based dive industry. A shift that also occurred with this move was more reliance on dive masters. To the credit of the dive industry they have kept accident rates low, but it has come at the expense of OW and AOW divers no longer being truly independent and capable of planning and conducting divers to the limits of their certs without a DM being around.
-----
As for nitrox being "safer" that really depends on the profiles, the gas consumption and to some extent the responsibility of the diver.
If a diver is gas limited where they run out of available gas before they run out of time remaining on the NDL, then yes, nitrox will have them surfacing with their tissues less saturated and it is arguably safer in terms of DCS risk.
However, if the limit is bottom time, and nitrox just extends that bottom time with the diver surfacing with a longer NDL but with similarly saturated tissues after the longer bottom time, then it is at best a wash.
And nitrox does carry with it increased risk of oxygen toxicity and it requires discipline in terms of respecting the MOD, monitoring depth, analyzing the gas, etc.