What 13.5-inch guns would have changed for Dreadnought

How much difference would 13.5-inch guns have made to an alternative HMS Dreadnought?

They would have made Germany's claim that its high-powered 11-inch gun matched Britain's armament much harder to sustain, although British fuse problems would remain.

The Kaiserliche Marine could plausibly argue that a high-velocity 11-inch gun competed with Britain's 12-inch weapon. A 13.5-inch British shell was visibly and materially larger, making that political and technical claim far less convincing. The change would therefore increase the cost and difficulty of Germany's response as well as the ship's direct firepower. A larger caliber would still leave unreliable British shell fuses uncorrected.