I like the darker stained one as it goes well with the bit of color I can see in your living room area and adds some interest. Though yes, painting them white would make the space feel more open. I don't think you can go wrong either way.

Since you have only two and they're perpendicular, I think the best thing is to paint them to match the ceiling. They don't make sense to me when they stand out. If you want a wood accent on the ceiling, add more beams in a coherent pattern.

I think, either way is ok. Stain light one to match dark, or paint them both white. Use a good quality bonding sealing primer on both. Regular primer would probably work on the light one that has no stain, but, the stained one needs the better primer.

Normally I prefer a wood beam. Something here just seems a bit odd. Are they there for an actual reason ( Is there a header or electrical running through them?)? They seem short for being header beams - maybe they are decorative and you could remove them? ( Although that textured ceiling could give you an issue ) .

I think I would paint them to match the ceiling.

If these are decorative beans then remove them. They don’t make any sense . Other paint to hide them

@User thanks for your input. What issues are you referring to?

Looks like an attempt was made to use the beams to delineate the dining space from the rooms on each side. The beam color near the kitchen seems to match closer to the shelves on the wall, and the beam near the living room goes with the darker stuff in there. If you're after a look to feel more open, then likely should be painted to match the ceiling

Post more pictures of the spaces. Ceiling pics don't tell the full story.

Do you know how difficult it would be just to remove them? If that's not possible I would go with painting them like the ceiling.

The question to ask is if either of them are load bearing and holding up the ceiling and keeping it from caving in. Sometime if walls are removed to open up space theyll put in a structural beam like that, supported at the ends, to take the place of the wall in holding up the floor above. In that case you wouldnt want to remove it! Or maybe they are concealing wiring or plumbing? If just intended to be purely decorative - it really is kinda odd , usually theres a whole row of decorative beams across the ceiling meant to look structural not just one or two. Assuming they could be removed without ceiling caving, I would remove at least the one next to the kitchen - the placement of it is kind of odd. Maybe leave the stained one but maybe drywall it in, then paint, and make it read as part of the wall, to serve as architectural element dividing kitching/eating space from the living room.