Explaining change in PhD project
Just be direct and honest: you wanted to do more theoretical work in your project and, as you said, you mutually decided a different project and program was in your best interests. There's no reason to try to hide the fact, and mention that your former advisor was fully aware of and supportive of your request. That should satisfy any concerns that you're doing it because you didn't get along with your advisor or because your project failed or anything like that.