Yep, the chambara films were like westerns too. Thats probably why they were so easy to adapt into films like The Magnificent Seven, A Fistful, etc.
I always thought Mad Max was sort of influenced by the spaghetti westerns. Substitute the SW anti-hero for Max, horses for cars and the whole outlaw nomad gangs for bandits. Even the atmosphere in Australia recalled the the terrain of the SWs. Desolate and dusty.
Im pretty sure the kung fu films were inspired by the SWs. They even lifted alot of the scores from them. Tales of revenge, the country settings, colorful villains, switch martial arts for guns. They are similar in alot of ways.