The Short Answer
If you want to see Mount Fuji, go to Kawaguchiko. If you want an onsen and a day of scenery, go to Hakone.
This is not a close call, and the reason is geographic rather than a matter of taste.
Kawaguchiko sits on the north side of Fuji, in the Fuji Five Lakes, with the mountain directly across the water and nothing in between. The classic images — Fuji reflected in the lake, Fuji behind the Chureito Pagoda, Fuji over a thatched village — are all taken here.
Hakone is a volcanic caldera about forty kilometres south-east. Fuji is visible from parts of it, notably across Lake Ashi, but the crater rim frequently gets in the way, and even on a clear day the mountain is further off and smaller in the frame. What Hakone has instead is hot springs, a genuinely enjoyable transport loop, an open-air museum and a sulphur valley.
The two are marketed together because they are both day-trip distance from Tokyo, which has led an enormous number of visitors to book Hakone expecting Fuji and come back without a photograph.
A third answer that is often the right one: do neither as a rushed day trip and take a guided day that covers the north side properly — our two-sides day tour covers Chureito Pagoda, Oshino Hakkai and Owakudani in one.

Mount Fuji Two Sides Day Tour: Chureito Pagoda and Oshino Hakkai
A top-rated Mount Fuji experience, bookable directly through AsiaByLocals.
From USD 59
10 hours
