Dimension Sword vs The Luminary: who would win?

The Luminary favored — Slight edge (~55%)

Dimension Sword · Dragon Ball · Base

Tier
2-C
Attack Potency
Low Multiverse Level
Speed
Immobile, up to Infinite
Durability
Low Multiverse Level

The Luminary · Dragon Quest · Act 3 and Post-Game

Tier
2-C
Attack Potency
Low Multiverse Level
Speed
Massively Hypersonic, up to Massively Ftl+
Durability
Low Multiverse Level

A heuristic estimate from normalized VS Battles Wiki stats: tier, attack potency, speed and durability.