I don't know if there's such a thing as Pure sandalwood, they're all different, and you either like them or not - and then thre's the fragrances, some of which are unrecognisable of whatever Sandalwood is supposed to be.
A true Sandalwood Essential Oil has a particular scent, but that scent is not what most of us know as Sandalwood. Unfortunately there is much adulteration of Sandalwood, many brokers will dilute it with carrier oils like jojoba, or even add synthetic fragrance to mask their work. Sometimes they will add a lower quality Sandalwood-like scent such as Amyeris.
There are also 'other' Sandalwoods - Red Sandalwood, Australian Sandalwood. None smell quite the same, but have uses in cologne-style blends.
That said, what you smell in TOBS sandalwood is not a pure Sandalwood at all. It has a very synthetic twang to it, plus I believe there is some incense in the blend. It's sweet, a bit powdery and not "Sandalwood", but a mighty nice scent that my nose likes.
Proraso Red is a very pure 'straight' Sandalwood scent, however I doubt it is 100% pure Mysore Sandalwood Essential Oil based. It does have a good dose of Mysore, could be as high as 30% of the fragrance component. The rest is probably something like Amryis. I can't detect any noticeable synthetic note in it, and my sister who has very sensitive skin when it comes to synthetic product shows no sign of irritation.
For the money you pay, the lather you get and the scent being such a 'straight' yet earthy, masculine Sandalwood scent, I reckon the Proraso guys have hit a home run. Waiting for the Pre/Post to come out in the Red version.