Would 8.3-inch guns have helped Admiral Hipper?

How much more dangerous would Admiral Hipper have been with 8.3-inch guns?

Not significantly; Hipper's limiting problem was achieving hits, so a modest caliber increase would not have changed the engagement much.

A modest increase from eight- to 8.3-inch guns would not solve Hipper's difficulty in achieving hits. Heavier or faster shells would matter only if they struck their targets. Lützow's performance raises the same issue: no hit is conclusively identified as an 11-inch shell in this assessment. The damage to Achates is considered more likely to have come from Hipper, while an 11-inch hit remains possible.