I'm pretty familiar with TM1 (because we sell and implement it). It is a genuine real time calculation engine and thus especially good for tasks like budgeting, forecasting and modelling. Typically it is set up and run by finance types rather than IT and the normal delivery method is Excel.
It is _very_ different from BO - more powerful calculation capability, arguably less fancy UI (but Excel users love it to bits). There are those who suggest that the two would go well together.
I hope this post isn't breaking the site rules but I can't help observing that 95% of the posts here are about the MS offering and good as that is for certain jobs there are many alternatives out there and I'd like to see some of them get some coverage for a change.