The 6.5 Carcano is a perfectly suitable round for medium game, or for bigger critters like elk at moderate ranges. Not terribly fast and not benefitting from the development of typical .264" caliber bullets, those old heavy-for-caliber RN pills penetrate disproportionately to what the ballistics suggest.
Hornady makes a 160 gr. RNSP that is reputed to produce very good accuracy, and Norma produces a factory load with a 156 gr. RNSP. PRVI has a couple of offerings, and they're way cheaper than Norma, but I've never heard anyone accuse that ammo of being accurate.
A lot (most) of the stigma around the Carcano is due to it's historical significance here. The rifles and the round really aren't bad at all. The 6.5mm 91/38 short rifle is a fast handling, light weight critter with perfectly acceptable accuracy. Frankly, if we're choosing between WWII military rifles to carry through the woods for hunting, the M91/38 would come out ahead of most others for me.
Really the only downside to them is that they are single shot guns if you have no en bloc clips. On the flip side, they reload faster than any stripper clip rifle, and without tearing up thumbs.
like the other carcano it is not quite fitting the "normal" 30 cal bullets.
The 6.5x52mm is a "not quite" at .268" vs. .264". The 7.35mm is a "not at all", as it's a .29 caliber round, bullets a full .010" to .013" under any 7.62mm/.30 cal cartridge of any other nation.