Glad to see you again, it is also a great opportunity for me to reacknowledge the grammar and expression in Japanese.
(A) 人生は短すぎる。 (B) 命は短すぎる。 Both are grammatically correct, but meanings are somewhat different and (B) is less common.
「人生」 is, so to say, "One's period from birth to demise". The translation (A) means "One's life is too short to experience everything" and would correspond to the given sentence in English. In this sense, we do not say 「命は短すぎる」.
「命」 usually means "physical life". The translation (B) is used only in a special situation. For example, when somebody passed away at a young age, a funeral attendant may say 「命は短すぎる」 (How short life is!), mourning his/her death.
Just for reference: a quaint and poetic example of 「命」. Thanks for the good suggestion, Neamhain. A proverb 「命短し恋せよ乙女」 (Girls, fall in love. Life is limited.)