If I could find a big enough stand bag that would be my choice, I do not own a push cart and don't intend on buying one. I like the stand bags when I do walk but I ride more because of the courses. Im probably just going to get a cart bag, the one I have been looking at seems to stand fine on its own.Cart bags typically offer more storage space and have a few little extras. Stand bags are typically lighter, but don't have as much extra room.
I've always been in favor of the larger stand bags. I rarely walk, but it is nice to have a walking/stand bag if I do. It might be a little bigger and heavier to carry than some, but not that big an issue. I like having a bigger bag so I can pack it with stuff that I might need, especially when I am riding. Plus it is easier to carry it to the range, get in and out of the car, and since it has the stand, you won't ever have to lay it down.
I would probably prefer cart bag for the storage, but I like having the leg stands so I don't have to ever just lay it on the ground. Especially in the parking lot. Some are big enough they will stand on their own, but if it is on a hill, they might not.
Overall, I think you can get a stand bag that will be versatile enough for both uses, a cart bag really only has one use.