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Michael Cohen, a former personal attorney of President Trump, in recent testimony before Congress, stated he would not accept a presidential pardon. Is this an option he has? If a pardon nullifies a committed crime, it seems like he should not be allowed to choose if he goes to prison or not because as far as the federal government is concerned, the crime is forgiven. An average person could not go to prison if a jury found them innocent. Why is this different?

It is possible to reject a pardon. Referring to United States v. Wilson:

There is nothing peculiar in a pardon which ought to distinguish it in
this respect from other facts; no legal principle known to the court
will sustain such a distinction. A pardon is a deed to the validity of
which delivery is essential, and delivery is not complete without
acceptance. It may then be rejected by the person to whom it is
tendered, and if it be rejected, we have discovered no power in a
court to force it on him.

There are also other practical effects to accepting pardons, such as waiving of fifth amendment rights relating to the pardoned crimes, since it would be impossible to self incriminate anymore. So there are reasons to refuse beyond "choosing to go to prison".

The question is theoretical. But there's no need to theorize. There's at least one case of a convict successfully rejecting a presidential pardon. The Supreme Court ruled on this case in 1833, saying a pardon is "not completed without acceptance".

The case is touched upon in a previous answer to this post.

Here are excerpts from an article describing the case:

The Man Who Refused A
Pardon ~ CBMC
International

In 1829 two men, George Wilson and James Porter, robbed a United
States mail carrier. Both were subsequently captured and tried in a
court of law.

In May 1830 both men were found guilty of six charges, including
robbery of the mail "and putting the life of the driver in jeopardy."

Both Wilson and Porter received their sentences: Execution by hanging,
to be carried out on July 2. Porter was executed on schedule, but Wilson was not.

Influential friends pleaded for mercy to the President of the United
States, Andrew Jackson, on his behalf. President Jackson issued a
formal pardon, dropping all charges. Wilson would have to serve only a
prison term of 20 years for his other crimes.

Incredibly, George Wilson refused the pardon!

An official report stated Wilson chose to "waive and decline any
advantage or protection which might be supposed to arise from the
pardon…."

The U.S. Supreme Court determined, "The court cannot give the prisoner
the benefit of the pardon, unless he claims the benefit of it... It is
a grant to him: it is his property; and he may accept it or not as he
pleases."

Chief Justice John Marshall wrote, "A pardon is an act of
grace, proceeding from the power entrusted with the execution of the
laws... (But) delivery is not completed without acceptance. It may
then be rejected by the person to whom it is tendered, and... we have
no power in a court to force it on him."

^{(emphasis mine)}

Reference:

• United States v. Wilson, 1833

Certainly in the UK at least one person has refused a pardon, on the grounds that accepting the pardon implied their accepting the guilt of the action in the first place. They were attempting to prove they did not commit the act in the first place.

There is a difference between 'you did it but we forgive you' and 'you didn't do it' and the person wanted to prove they didn't do it. The same could hold true for a presidential pardon, but I suspect that Michael Cohen, having admitted his guilt, is making a different point.