I would go with white.

Wood is en Vogue right now and is classic, So I would leave the wood alone. The present wood kitchen looks much better than both of your renderings.

To update this kitchen, paint the walls Benjamin Moore’s Swiss Coffee. Bring in under cabinet lighting. Cabinets don’t appear to have hardware. If you add any hardware, make it black. And clear out the clutter. That will update the kitchen. Your other two options will not only destroy quality, on trend cabinets - but they will look horrible and will not work with the floor. And I would leave the wine rack; it’s a novelty,

Painting, especially a “quick” paint job, is going to make those cabinets high-maintenance. You say this is a rental, but don’t specify if you’re the landlord or the tenant. If the former you will end up repainting those cabinets between each tenant...not something I’d want to do. If you’re the latter you’d best be very sure you have your landlord’s written permission to paint them, and be aware they will look crappy quickly unless you pay a pro to do them right.

But @freedomplace1 is right, the cabinets as they are now look MUCH better than either paint option. The kitchen would look better overall if you’d change the open shelves to some kind of closed storage and did a good decluttering of all the surfaces. It’s a nice kitchen!

Leave the wood, it has warmth. The black as and white versions look cold in comparison, and every time their paint is nicked, the wood will show through!

For a rental, keep it simple: It's WAY easier to paint the walls than the cabinetry! I'd paint the walls a soft sage green color, as it would look nice with the wood tones. Color combo example:

Also, I agree with @freedomplace1's suggestions to add dark hardware, undercabinet lighting, and clear the countertop clutter.

Thanks everyone!! I won't touch the wood! I'm the owner. The place is actually empty now- between tenants, so no clutter. I think the one thing I will do is add a shelf above the sink. I think the bare area looks weird. I'll take a look at that BM paint color too- thanks for that.