theyre a form of industry validation- if you care about that, then yes theyre important.
metacritic is also a form of validation. it makes no sense to care about one and not the other
Grammy's are important. Artists care about Grammy's. They treasure their wins and are honoured to win them unlike other awards. No other industry awards is more important to a musician. When artists win Grammy's they are subsequently referred to as Grammy Award winning artist X. Let's put it this way, no musician dreams of winning a Kid's Choice Award!
Metacritic is just a website where randoms give opinions. It is completely unimportant and about as prestigious as an atrl poll. Comparing them to the Grammy's is quite deluded really. It is like comparing Meryl Streep with Kim Kardashian.