Solid wood doors were in almost every MCM kitchen ansds tood the test of time so I need to know what style you are going with for sure.

Two things you need to know about solid wood.

1. Wood moves. You cannot stop it but you must allow for it. It is anisotropic. I tell people it's analogous to people putting on weight. If I put on 50 lbs, I would not get much taller. Wood expands (and contracts) minimally in length (along the grain) with absorption (and desorption ) of moisture. It will expand and contract more in two directions, (a) radially, from the center of the tree out and (b) tangentially, along the growth rings, i.e., around the circumference. For most woods, the tangential is approximately double the radial. This is why if you see some dried firewood, you'll usually see a pie-piece shaped crack/void. It's also why plain-sawn wood can cup. If I put on 50 lb, I'd probably put on a significant "beer belly" (front to back) and a little bit less of "muffin top." (side to side) This is why you would never put a solid door inset into a cabinet. In the dry season, it'd have a big gap and in the wet season you may not be able to get it open. As to whether or not it might warp, it depends on how the wood is chosen and what the grain pattern is like. Quarter-sawn wood will have maximal expansion in thickness and minimal in width and less tendency to warp, other things being equal.

2, Wood has planes of weakness and planes of strength. Did you ever see martial arts hit a piece of wood and have it break? Did you ever notice that the grain is running up and down and not between the hands supporting it? Otherwise, they could probably never break it. The wood is weakest up and down the tree. In your second scenario, the grain will be running perpendicular to the rails (horizontal pieces) and if that's only a couple inches wide, it will be very weak. Compound that with the expansion issue above and this is not an option I would ever choose.

That is why the "5 piece" AKA frame and panel, is the most common construction method. The rails and stiles have maximum strength and minimal cross grain expansion. If the panel is plywood or some engineered wood, it will have minimal expansion. If it's solid wood (AKA raised panel) then its expansion and contraction is within the stiles' grooves.

Solid wood doors often have internal expansion joints and battens on the back to retain them.

Engineered woods do not have these issues. Sometimes a sheet, say MDF, is routed out to look like a raised panel, but it's really still just a sheet of MDF. If the corners are rounded and not square, that's the tip-off.

https://www.popularwoodworking.com/wp-content/uploads/2010/10/WoodMovement.pdf

https://www.thisiscarpentry.com/2010/09/03/moisture-content-wood-movement/

Like byhammerandhand said.