Learn English – Colloquial way of saying ‘I choose’

There are a few phrases that you can use, such as in place (of), instead (of) (also stead), to express the "doing something for somebody", depending on the context.

In any case, the phrase for someone doesn't have to mean that the person you do something for must be lazy. This, again, depends on the context. Compare:

He asked me to do his assignment for him.
I offered myself to do his assignment for him.

Here are some examples of in place (of), in someone's place, instead (of), and stead, I found on the web:

John came to help in place of Max, who was sick.
When the king's cloaked challenge is answered, Fluellen stands in place of him, representing him, and receiving the blow.
She knew she should not have sent him to work in her place tonight.
"O king, take my life instead of hers. Let me die in her place," he pleaded.
... it was Judas who was crucified instead of him, ...
... she had to ask their family doctor to prescribe instead of him making it available to begin with.
Take me instead! Not my boy!
The chairman spoke in her stead.
The marketing manager was ill and her deputy ran the meeting in her stead.

So, you can say any of these followings (choose wisely, register is important),

He asked me to do his assignment for him.
He asked me to do his assignment in place of him.
He asked me to do his assignment in his place.
He asked me to do his assignment instead.
He asked me to do his assignment instead of him.
He asked me to do his assignment instead of him doing it himself.
He asked me to do his assignment in his stead. (formal)

I'm afraid your two options are not equally good. :)

Although "as good as each other" makes grammatical sense, we rarely compare things like that. We usually say "equally X" to say that they're equivalent.

Intuitively, I think the two forms have different purposes.

When you say "X is as good as Y", the purpose is to use Y as a point of comparison to tell how good X is.

Mmm! This cake is as good as the one you made for my 40th birthday. That one was amazing.

A cheetah can run sixty miles an hour. That's as fast as a car!

If this is the purpose, then it isn't helpful to say that two things are "as X as each other". Take "The sea is as black as night." The purpose is to use night to show how black the sea is. Night is your point of reference; you learn how black the sea is by considering how black night is.

So if I said, "The sea and night are as black as each other," we have a problem. "Each other" means that you learn how black the sea is by looking at the night... and you learn how black the night is by looking at the sea. That's a circular comparison, and not very helpful!

But the purpose of the word "equally" is the purpose you want.

"Equally" doesn't say how good two things are. It only tells you that they're equivalent.

It affirms that neither is faster or slower than the other — that there is no point choosing either one on the grounds of how good it is.

(You can also convey this message by saying that X is "no worse than" or "no better than" Y.)

Although Ngrams are not always useful, they can give us hints. Compare the rate of "equally good" vs. "as good as each other" in this Ngram. "Equally good" occurs 100-1,500x as often over various decades, which is such a high ratio that "as good as each other" is shown as a flat line by comparison.*

_{* Keep in mind that Ngrams are useful but not always definitive. See this discussion on ELU. It certainly doesn't mean there are zero occurrences of "as good as each other", and it also doesn't include similar wordings. For example, the classic children's book Onion John, which is full of idiomatic American English, says this in chapter 18: "Onion John could no more disappear out of Serenity, everyone agreed, than the courthouse could get up and wander off into the night. One was as much a fixed and regular part of town as the other."}

Extra note

As a minor caveat, sometimes you will hear "as" used to mean "equally" to contrast with another comparative on the spur of the moment, and it will be stressed there. Here's an example:

— "Would you say Amy is friendlier than Matthew?"
— "Hmm... no, I'd say she's as friendly as Matthew. They're equally friendly."

If you want to say that she's not very friendly, you could say she's "only as friendly as Matthew" – but this makes Matthew the standard against which to measure Amy, consistent with the above.