Pass away - I agree that this is a more formally used phrase
Kick the bucket - This one is used quite commonly as a colloquial dysphemism (making it sound harsher than it is - avoid this at a funeral it may offend someone.
Meet one's end sounds more philosophical to me, sort of like implying one's death was part of their destiny.
Depart this life seems more spiritual, quite good to use when in the company of religious believers in my opinion.
Bite the dust - Quite like 'kick the bucket', this is another quite harsh dysphemism, again, if you are at a funeral, definitely do not say this one
Have left us - This one seems more of a term to use when discussing a friend or family member. To me, it sounds a little resentful of the dead person, so be careful if you were to use this.
Went to sleep appears to be used to mean someone literally died in their sleep, also could be used similarly to 'pass away', to demonstrate a painless and peaceful death.
Decease - Very common term. It is the most formal word to mean death, I would say this is very clinical, much like what a doctor would use to describe a death.
Lose one's life - like losing an object, it is unintentional, so more attributed to an accident or a death that is someone else's fault rather than any other sort of death.