Within 150 yards, the advantage goes to your comfort with the platform.
The .30-30 will probably be launched by a lever-action Winchester or Marlin. That's a good woods-walking rifle, quick handling and quick to bring a second round or more towards the target. It was never intended as a battle rifle to engage enemy targets way out there. I'd have no problem using a 150 or 170gr .30-30 load to put venison on the table, as long as I kept my shot distances reasonable.
The 6.5x55 would probably be launched from a bolt-action rifle, perhaps a surplus M98 or M38 Swedish Mauser, or a Tikka, Sako, Ruger, Remington, Ruger sporting rifle. It could also be launched by an AG-42B Ljungman, but even I don't take my Ljungman out hunting. (I should sometime, no real reason not to)
The 6.5x55 Swede was intended as a military cartridge, designed to engage enemy targets, with a battle zero for the M96 rifles
beginning at 300 meters. So for close-in engagements, say for 100-150 yards, you do have to aim low if you're using an as-issued M96 Swede Mauser. Is the round suitable for hunting within 150 yards? By all means. Many years ago, I took a whitetail from 45 yards in a Wisconsin cornfield with a military surplus Swedish Mauser. I hit the doe between the eyes as she was looking at me, head-on, removing everything above the nose. Messy, but I had a freezer full of venison.