Benefactive Action (Doing X As A Favor)

Someone did something for you, and you are deciding which of you is the subject of the sentence.

Verb て もらう vs Verb て くれる: Both describe the same favour. てくれる makes the doer the subject (友達が手伝ってくれた), and てもらう makes you the subject (友達に手伝ってもらった). てもらう also implies you asked; てくれる leaves it as something they did of their own accord, which is why it sounds warmer.

You want to offer to do something for someone senior to you.

Verb て + さしあげる vs Verb てあげる: てさしあげる is the humble form, but it is risky: announcing your own favour draws attention to it whichever form you use. In practice offer with ましょうか instead, and keep てあげる for equals and てさしあげる for describing the act afterwards.