I respectfully disagree with your assessment of which direction would be best.
As to the OP's concern about wood splitting along growth ring lines, there's not a whole lot of info out there about that. Perhaps I'll head to my wood shop and do some experiments.
Hold on please .... we are mixing two different things: strength versus warping potential. Lets please not confuse the two and start getting into flames owing to misinterpreting what people are saying.
I would tend to agree with what WEO said in terms of his "green" cut - that it would be better from a strength perspective, **but** he did make the point of cutting thick enough to accomodate for warpage before flattening (at least that is what I read him to be saying). (if you look at that cut and the way the growth rings are arranged - it is kind of like plywood - laminated layers that would make the piece strong against bending).
If you look at WEO's "yellow" cut, you do **not** end up with that "laminated" grain structure, and so you lose the strength against bending that the laminated structure gives you. At least with some woods, this "quarter sawn" grain structure makes the wood definitely weaker against bending when the bending could cause the wood to break along the length of the grain.
My son is a third-degree black belt in karate. they break boards. If you look at videos of that being done .... you will see that they **always** hold the board on the sides where the grain runs lengthwise along that side - and the board ends up breaking along the length of grain. If they hold the board the other way, they are basically trying to make the board break **across** the grain lines .... and broken hands (not boards) result.
so my question was, for knife handles, is this grain structure still sufficiently strong?? I think Horsewright answered this question. I do think that WEO's "green" cut would be better/stronger (owing to the resulting laminated grain structure) - but only after allowing it to dry and then flattening to compensate for that warpage.
(BTW - these pieces are at 8-10% moisture - which is pretty close to equilibrium that I see for denser woods - though into the drying cabinet they will go!)