Yes, you can build a car that will work for both. A few of the short course SR1 racers have also done the BITD race. But a purpose built car specifically for that style of racing will work better. But it will be easy to build a desert specific car that will be legal in all the big and small desert events. SCORE has the strictest rules, so I would build for them and go from there.
UTV racing in SCORE is only Sportsman, so they let you make some changes that you can not do in the PRO class in BITD.
What kind of car are you building?