That's not the way I recognise it.
As far as I'm aware, the proper M models (not M-Sport) get their own gearboxes (DCT).
The older models like the E60 / E90 (like you linked to above) have the older ZF 6 speed box, the one I referred to as sluggish, and using fuel. I had this in my 335d, and while it wasn't bad, it wasn't impressive either.
The newer models have the ZF 8 speed, which is a fantastic gearbox. And can come with or without the Sports "map". I have this in my 530d in Sports Auto guise. And is the gearbox I referred to as "wouldn't want a manual instead" above.
Personally, if you have the budget to go for the F10 over the E60, I'd do it. Without hesitation. It's a far superior car.
As said above, the M-Sport is a different trim level rather than different mechanicals. The only real mechanical difference is the M-Sport springs. Other than that, it is bumpers, steering wheel, seats, headlining etc... Personally, I'd rather have the M-Sport, but probably not at the cost of certain spec. For example, I'd probably be happy enough with an SE if it had Pro Nav, decent speakers, reversing camera, black panel display etc... That sort of stuff. But if it's just a poverty spec SE just to get into the newer model, I'd maybe reconsider.