Installing a pet door in your wall can be a great choice. You can have a lot more flexibility as to where it goes. You can also patch the hole in your wall if you want to sell your house down the road. That said, wall dog doors are not for everyone. Unless you are particularly handy, we recommend having a skilled contractor install it for you because it does involve cutting a hole through your wall.
Security can be a concern with any doggie door or cat door, but one handy trick is to put a doghouse on the other side of the doggy door. This conceals the dog door from would-be thieves.
Another benefit of the doghouse is that is prevents needing ramp for your dog door for wall. Most wall entry dog doors need ramps since the floor in your house is higher than the ground outside of your house. The doghouse reduces that difference.