Seems like an either/or type of choice. So it would depend on what you want. Here are my initial thoughts.
AR10 in 243win - with a 10 twist barrel the heaviest bullet you can shoot is about 90 grains. That's a larger enough bullet to kill deer if you decide to go dual purpose. Also, the 243win is not a barrel burner.
AR15 in 243wssm - with an 8 or 9 twist, you can shoot the 105grain bullets. The wssm though is a bit of a barrel burner.
I had the same problem. I went with the 243 wssm in the ar15 frame for the significant price and weight difference. (Went with a dtech upper with select shillen barrel for ~$900 and a rock river complete lower ~$300. The rifle's primary use will be coyotes, so the weight was definately a priority. One thing about the wssm is the magazine will limit you c.o.l. with longer bullets.
Not sure why everyone thinks the wssm will be any more of a barrel burner than the winchester. Shoots virtually the same amount of powder.