I personally think 「恵み」refers to a gift from God, nature or someone. On the other hand,「祝福」refers to well-wishing or celebration. Listed below are some examples:
Hey dude, I'm not in the mood to be celebrated:
祝福される気分じゃないな
Thank the land for its blessings:
大地の恵みに感謝する
Are you a Christian? If so, the words are often used with the similar meaning at Mass. Listed below are some examples of the words in the order of the mass:
May almighty God bless you, the Father, and the Son, and the Holy Spirit, amen:
全能の神、父と子と聖霊の祝福が皆さんの上にありますように、アーメン。
The grace of our Lord, Jesus Christ and love of God blah blah blah…:
主イエスキリストの恵み、神の愛、何とかかんとか…
I hope this may help you.