Pitting Stardew Valley against Harvest Moon (Natsume's Harvest Moon, old and new) is like demanding a grandparent fight their grandchild. Without Harvest Moon, there would be no Stardew Valley. However, there's also no denying that Harvest Moon has lost its way over the years.
You could argue the best Harvest Moon is Back to Nature, 64, or Friends of Mineral Town.
Harvest Moon 64 improved the graphics in a meaningful way, added a memorable soundtrack, and Back to Nature added further depth to the game and the characters of Mineral Town, and FoMT did it all again in a slightly different and even more robust flavor. Farming was the core focus, and everything still felt fresh in the series.
From there, things started to deteriorate a bit. A Wonderful Life and Hero of Leaf Valley, along with Save the Homeland, were interesting ways to add a different sense of accomplishment — though why someone thought making you die at the end of AWL was a good idea is beyond me. Still, they missed the point of a Harvest Moon game in the process by centering them around a definite point.
Later entries were fun, if iterative, including Sunshine Islands and Grand Bazaar. The last good Harvest Moon was A New Beginning, which despite not doing a whole lot to shake things up did at least include new design and customization mechanics.
Part of the issue is how Harvest Moon hamstrung itself with the adventure hybrid series Rune Factory, relegating the base series solely to farming with Rune Factory taking the more dynamic approach.
Today, the Harvest Moon we get in North America and Europe isn't the Japanese series Bokujou Monogatari, as it's traditionally been. Instead, recent Harvest Moon titles are unique games developed by Natsume, rather than the Marvelous-developed series we've all come to know and love over the years.
In the West, Bokujou Monogatari (which used to be called Harvest Moon here) is now called Story of Seasons, and that's seen its fair share of changes as well.
Harvest Moon: Light of Hope shows how that all's been going.
Stardew takes advantage of all those different styles, then wraps them up in the simplicity of an older Harvest Moon game. You've got the dungeon exploration aspect, farming, socialization, quirky townsfolk, building, and customization.
There are several, varied goals to work towards as well if you want to restore the Community Center, which goes a long way in keeping things interesting.