In each of the poems the speakers want to be overcome by something. One wants death and one wants life - life without sin. Although Sidney's speaker bribes death and Donne's speaker promises to repay God for his help, it begs the questions: is it likely that both speakers will really pull through? Do they really want what they're asking for? Or do they think that just by pleading, they are perhaps proving something? Or really asking for the total opposite? What are their true intentions?
It seems as though the only time each speaker can achieve their goal is when they get what they are begging for. Neither can have what they want, and both need release. As Sidney's speaker describes death as "being thine by right," Donne's speaker says that he is unworthy of God and purity. This is ironic because in a situation like this, where one begs for God's help or the help of anyone for that matter, you would think they would have confidence in themselves or at least make believe that they are worthy of receiving the help they are asking for.
If one asks for help yet admits his unworthiness, why would whoever he is begging for help want to help such a person, who doesn't even believe in himself?
Maybe Donne's speaker is telling God that although he is unworthy now, he is willing to do anything to get God's help and to become worthy or, even though both speakers convincingly beg for help and a savior, maybe their intentions are the complete opposite of what they seem. Maybe Donne's speaker thinks that just asking God for help is enough and because God has obviously not helped him yet in his life, even if he begs...