3-1/4" is generally more stable since it's narrower and should have more fasteners. 4" may cost a bit more but it has a slightly better visual pop. Essentially they are both what I'd call a "background" floor that lends a quality look to your home without competing with other design elements.
Red Oak is more uniform in color and has a red/orange hue.
White Oak is slightly harder and less grainy, has more color variation and more of an almond or taupe cast.
Both can be stained but White Oak produces richer brown stain colors. Red Oak can be very grainy looking when stained dark.

Thanks for the information!

I think I'd prefer the visual pop, and I am staining it dark..... so seems like 4" white oak is an appropriate choice!

Thanks!