I have a custom 7STW that shoots great and was my "go to" rifle for quite awhile. Given that the two cartridges have nearly identical case capacity and ballistics; why choose the wildcat which will cost you more in the long run and be harder to sell if you decide to get rid of it in the future? Go with the 7STW.
However, seeing that you're not limited to just those two, why not consider the 7RUM? Quality brass is now readily available, which is usually a big consideration when choosing a cartridge for a new custom build. The 7STW will probably limit you to Rem brass which is arguably one of the worst available. I've heard that Win discountinued making brass in 7STW. You could make 7STW brass from other magnum cartridges (300Wby-300Win) but why would you want to go through that unless you have to?
Just my 2 cents but I'd give the 7RUM a good hard look and maybe even the 7WSM if you would like to extend your barrel life.