Sorry SteL, I missed the context earlier - busy-ish day.
But yes, it will probably go on warping/splitting roughly on a horizontal line where you have the handle (which is where the centre of the tree was). It depends on how much the moisture content and temperature of where you keep it differs from how it was when rough sawn and kiln dried.
I still use the bench I made by hand 30+ years ago. It has a rather nasty slab of Nemesu (Meranti subspecies) as the front edge/face, and one jaw of my face vice. The other, moving, jaw is a mahogany (can't remember what though). Even though I was careful to take off the arrises from the edges and corners, that's still 30+ years of having to stop periodically to tweezer-out nasty splinters from fingers, etc. The excitement of that does wear off fairly early on.
Mind you it looked lovely when it was first finished - all neat and with clean lines...
... So you can go too far t'other way too, and use a wood that's far too tough. Not sure what I shall use when I rebuild it, but I will give the matter some serious thought before committing to anything.
A slab of beech would probably do well, or ash, but bear in mind that woodworm love beech, too, for quite different reasons. So if you are planning to keep the bench, it's probably worth treating it with preservative (spirit-based), or putting a finish on, to discourage the little blighters and reduce the speed at which the moisture content changes. Try to find something that doesn't have obvious rings in the end grain - gentle curves are OK, but tight rings will bring issues.
Custard was commenting earlier - he'd be the ideal person to suggest what to use instead. That said, pine would probably be OK if it was cut from the tree differently. Beware of knots in pine though, because of the resin they have in them that they tend to share with everything they touch.
I should also say in fairness that the vice is a Record 52E, so the front edge of the bench and the moving cheek are thin and well "supported" by the cast steel pieces in use. Nothing has split.