I like them both, and in fairness to the WSK, I have many more cooks on the BGE having owned it for 12 years vs 10 or 11 months with WSK.
I like the BGE for the temp control. I can easily hold 180F and higher with very little adjusting, and when the temp stabilizes, it stays within a few degrees. The WSK is not as stable for me and I have to fiddle with adjustments more.
On the BGE I love the PSWoo being able to remove the cooking grid and platesetter as one to adjust the coals. I like that part much better than the WSK. Adding another chunk of smoke wood is more work on the WSK when using the deflector.
I can increase temps fairly easily on the BGE but if I overshoot it's very hard to bring temps down. The WSK is much easier to move temps up or down and a short overshoot is easy to recover from and the WSK can easily move from 250 to 500 F.
the WSK is a much, much better grill. Part of that is a 24 inch grate vs an 18 inch grate. Grilling direct on the BGE is a pain because the grate is dropped down 3 inches or so. Two zone is simple on the WSK, and not really easy on the BGE.
I can do vortex on the WSK grill indirect at 450F. I can do dual side offset on the WSK.
The BGE allows raised direct which is close to vortex style cooking, yet that can also be done on the WSK.
Pizza on the WSK wins hands down. Not even close for 600F and above. The BGE can get as hot, but it is a beast to work with.
Ash cleanup is a breeze on the WSK. I have a kick ash can and basket on the BGE so with that add on they are about the same.
Moving the WSK is easy. Moving the BGE takes caution.
Add ons...
On the BGE I have a KA can, KA basket, PSWoo with extender rack, a drop spider and a heavy duty SS 14 inch searing grid for the drop spider. I also like the swing up side tables on the BGE.
The only add ons for the WSK are a vortex and a cast iron searing grate that fits into the GBS.
I've yet to make a mount to attach the smoke daddy to the WSK, and I hope to get to that soon.
In summary I love them both and am fortunate to have both.
If someone asked me to recommend one or the other, the WSK be my recommendation, especially if it was their only grill.