Both of these shows have now are in their second seasons and there is a rivalry with some of the fans of both these shows.
I have watched both of the 1st seasons and are now watching the respective 2nd seasons, I can say you can watch both shows with no issues as they are quite different.
The Orville initially looked like a comedy Sci- Fi show from the earliest trailers but watching it you realise it is trying to replicate Star Trek: The Next Generation with look and story telling. The show has slowly gotten better over the course of its run so far, finding its feet after an uneven 1st season.
Star Trek: Discovery which claims to be prequel show set 10 years before the The Original Series, looks pretty but was very uneven in the first season with several story lines and characters breaking continuity with Star Trek lore. The 2nd season has so far been dramatically better with the introduction of Captain Pike a character loosely from the original series, it appear the show runners are attempting a course correct to fix up some of the issues from the 1st season.
My advise is to give both of these show a try for a few episodes before making judgement.