I've never gotten around to watching The Orville. I'd like to and I guess I should some day but I never seem to find the time.
The dialog on DSC does seem to be a bit variable and I wonder how much of this is down to the different writers. The actors do seem to be doing their best to try to make their own characters consistent. So far, Doug Jones' Saru has been a real stand-out for me and Anson Mount's take on Pike has worked particularly well. I'm kinda liking Ethan Peck's Spock too.
The lines are definitely clunky at times but this isn't just a military-procedural show or a bunch of dry scientists in a lab. I've never been in the military but I am a physician and previously worked in uniform in EMS for about a decade (and I've spent time in academic labs); people are people wherever you go and, frankly, most of the time they chat and talk normally in ANY occupation. The difference is the professionalism and training that kicks in very rapidly when something unexpected or serious happens -- THEN you see the change in gear to very clear, precise communication with reference to safety checklists, read-back of orders, or whatever. Good people with good training can do that in the blink of an eye -- and then wind down and go back to "normal" when it's all done.
I can run a busy ICU with very sick patients who have extremely complex illnesses and lots of complex organ support -- but I can still chat to my junior docs and senior and junior nurses. I can be joking with our senior nurse-in-charge one moment but if a patient crashes or we get a critical new admission then it's all eyes on the task and hands-on. The communication changes instantly -- but that doesn't mean it becomes stilted or unnatural; it's the FOCUS on the task that is key (and, to be honest, it certainly doesn't prevent humor or banter creeping in either, even if what we're DOING is still absolutely on-point).
Now, hospital shows sure don't get this right (in fact, for me, their dialog can truly suck big-time as the writers play up the drama for the viewers) and I think you're seeing the same thing on DSC. Yes, Burnham is probably one of the more inconsistent here and the writers seem determined to keep playing Tilly for laughs or as just plain awkward without allowing her any room for professional development and growth. As a side note, she does remind me of some of my more nerdy junior docs but with support and coaching, they get more confident and calm down as they gain experience -- they need to allow Tilly to do the same or she becomes too one-dimensional.
The end of the last episode when Pike takes on Burnham's point about destroying Discovery to prevent Control accessing the Sphere data wasn't such a bad scene; yes, bits of it were over-played (or, rather, over-written) for dramatic effect -- but, nevertheless, there was a definite sense on that bridge of "oh, shit, this just became serious" followed by Pike returning to THE CHAIR (big visual cue...) and a pan round the rest of the officers to emphasis that "the Captain has just made a big decision and we're all about to get orders -- so we're paying attention."
All in all, I think DSC is slowly evolving; it's not perfect but it's kinda getting there.