Sauté meat then vegatables, or vegetables then meat?
Generally, browning meat is done at high heat, with a preheated pan well over 400°F, and will leave a bunch of tasty brown stuff (fond) stuck to the bottom of the pan. Vegetables contain a lot of water, which will dissolve the fond off the bottom of the pan, bringing its flavor in to the dish.

If you did it in the other order, you'd have maybe have some fond from the vegetables (depends on how long you cook them and how hot), which would burn as you brought them pan to temperature to brown meat.