That pretty much sums it up well. I've used both as well but from the "selling side". BMWFS is unique in that they allow leases to be assigned to a new leasee while removing the original leasee entirely from the contract, which is good for you in that you aren't tied to the original personal in any way once the deal is done (it's good for them as well, because if you stop making payments, they're not liable).

A couple of additional points:
1) the seller should pay the BMWFS transfer fee
2) make absolutely sure that the mileage is what they claim it is. Some shady people will advertise the cars as being under the mileage allotment when the either the actual odometer mileage is a lot higher or the allotment is lower than they advertise. Check the odometer and lease paperwork.
3) check for damage on the car, you're liable at lease termination for it, so if the car is beat up, you're going to have to get it fixed (wheel rash is #1 to look for, then dings or scratches)
4) make sure it doesn't have a tune or any other mod that was added post lease, all of them have to be removed at turn in.
5) get the vehicle checed at a dealer before finalizaing anything. make sure the warranty /maintenacne isn't void
6) make sure everything that is supposed to come with the car (spare, manuals, etc) is in the car, if not you'll have to replace it before turn in.

Good luck.

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