Sam, if the wood is good, cut some distance from the pith, dry (at EMC), and well sealed, I haven't had any problems or remember any difference in stability if I worked with the pith in a platter up or down. What might make a difference is if the pith side contains any juvenile wood around the pith - notoriously unstable.
I should say I've never made a platter with a completely flat bottom, always make some kind of foot, even if it's wide. I almost always seal/finish with multiple coats of "danish" oil (some type of polymerizing oil such as BLO, poly, and solvent), each coat dried for a day or so, up to maybe 8-10 coats total.
With the bottom completely flat all the way across like a flat disk I would be concerned about warping with seasonal humidity changes. Also, although kiln dried, the wood should, of course, be brought to EMC for the intended final environment before turning and sealing. I store all wood, turn, and apply finish in a climate-controlled shop. Regardless, I personally think sealing the wood properly is important.
As for preference, in general I prefer the Xs look over the Os, ESPECIALLY if the pith is not well centered OR if the plank is sawn slightly non-parallel to the pith. I try to pay attention to this at the sawmill.
Note the top/inside only has to be
very slightly dished to control the pattern. I usually start with dry 8/4 stock. Actually, I don't think I've ever made a platter that wasn't slightly dished on the top/inside since I like that look.
This was from a Sapele plank about 20" wide. The pith was close to centered across the width of the plank so I made "O"s, pith up.
These, about 14" and 19", are from different Sapele planks. The piths wern't exactly in the center so I thought orienting this way might be more interesting. Again, the top/inside is very slightly dished. (We use these a lot, even earlier today to take baked treats to a gathering.)
You might make a wild guess that I like Sapele! I have some Sapele planks that are over 30" wide I should probably use so they don't go the the burn pile when I kick off someday.
JKJ