Tough choice between the two and one couldn't fault anybody for their choice.
If you want rugged, proper heathland golf (yet still refined), WH is the place. If you want a genteel parkland course pretending to be a heathland course, SGH is the place. Both are of exceptional quality. I spose WH has the trump card of two 18s while SGH only has 27 holes with one 9 not quite up to par with the other two. Both courses have their disruptions; WH with the awful M25 road noise and marooned 1st hole and SGH with housing and wee roads cutting through the course. The houses too are very different. WH is quite common with no views of the course and almost entirely dependent upon the Braid legacy and the events it has held to create an atmosphere. SGH offers lovely views and nicer surrounds, but it is a bit ostentatious for my tastes.
I am not sure as a member I could cope with WH's road noise, it is so deafening on a few holes and always at least white noise. Other the hand, I think as a place to play in the winter WH has to be the superior venue because the turf allows for better drainage. I suspect too, in the summer WH can get humming like SGH can only dream of. I am not sure either club would entirely suit me, but between the two, all else being equal, I would probably plop for WH. In reality, I suspect costs and distance from my home would be the real deciding factors because its just about a dead draw between the two.