having used both over the years
I HAVE TO FAVOR THE 308, the slightly higher velocity of the 243 at about 2900 fps at the muzzle helps rapid expansion
the marginally slower 150 grain 308 at about 2800 obviously hits harder has more mass and depending on bullet construction, generally penetrates a bit better,
deer and even black bear those bullets , don,t have difficulty reaching the vitals and those animals are not that large or strongly muscled, nor are their bones that difficult to penetrate,
ranges tend to be well under 300 yards
many people make a mistake in selecting bullets that don,t expand reliably, you don,t need exotic, bullets common designs like a 150 grain, speer, sierra or Hornady bullet
like this picture properly placed is lethal
BUT POINT OUT THAT THE BULLET DESIGN YOU USE AND OF COURSE SHOT PLACEMENT WILL HAVE A HUGE EFFECT ON RESULTS
YES theres a noticeable difference in bullet expansion characteristics between brands, do some testing and youll see the differences
I generally find SPEER bullets to expand faster than HORNADY , and NOSLER ballistic tips somewhere closer to the speers on rapid expansion
but still penetrate well.

while either caliber works you can,t ignore pure physics the 308 hits about 45% harder
http://www.grumpysperformance.com/oct18/deer-anatomyghk.jpg

aim for area (B) on the link/diagram and you'll seldom have and difficulty


btw bullet weight in grains x velocity x velocity /450240= energy

so a 100 grain x 2900 x 2900/ 450240=1868 ft lbs at the muzzle for 243

so a 150 grain x 2800 x 2800/ 450240=2612 ft lbs at the muzzle for 308
not a huge difference but its well worth having in my experience

cross sectional area before expansion,

243 .046 sq inches

308 . .074 sq inches