Whichever you cut 1st you need backer blocks to stop any tearout.
Use a flat piece as the backer to start then when routing the ends use either a square piece or a piece cut to fill the slot on the back edge of the style or rail.
This should ensure a clean finish.
For the panel raising bit cut the end grain first then the next cut, with the grain, will clean it up, turn 90 degrees to do the next endgrain and so on.
NEVER try to raise the panel in one go.
Start with the bit low then raise it a bit after each 4 cuts til you get to the finished depth.
Panel raising bits are too big for safe use in a 1/4" router.
Most are 1/2" with a few at 5/16" but very few 1/4" bits.
Until I get a 1/2" router I will continue raising my panels on the table saw using a jig made for the purpose.