The menu board is the same outside as inside. I've done both but on the inside I had a certificate for management to sign. Outside you can stand at an angle and get a better picture. I always take a dozen pics from different angles then pick the best of the pictures.
Generally the drive thru person cannot see you at the menu board. If you'll notice their camera is near the order board and another menu board pointing down on the car below. I don't worry about being discreet at a menu board.
I'm very careful not to take a picture of a customer even if I have to wait awhile. And I generally wait in another parking lot so I won't be seen.
I do a lot of this type of audit and so far I know I have not been seen taking a picture of an outside menu board. The good thing about doing a picture of the outside menu board is you can go any time of the day. My preference is before sun down so there is more shade but before dark so the flash is not seen by anyone.
I did one not long ago and it was pouring down the rain, humidity was 100% and my camera was fogging. I went at different angles taking loads of pictures since I was sure they were not going to look good. But they turned out great!!