You've already got two different sheens; does it bother you?

Well, we haven't noticed it being a big difference but we haven't moved in yet and the doors are black so it's really the color contrast that stands out over the sheen contrast.

I think it's fine for them to be different. You could always sample one in semi and one in satin so you can assess before you commit.

I wouldn't want my doors to be shiny!

I recently painted the trim white, and I didn't think I wanted sheen, so I began painting the trim in Simply White eggshell. But it looked dirty and dull, I hated it. So I switched and did the rest of the trim in the semi gloss, and did the doors in semi-gloss too. Much better. All the walls are still matte or flat, which I love. No, the two different sheens in trim and doors are not obvious or noticeable, but I think trim and doors in semi gloss just looks cleaner and brighter.