Bokmål or nynorsk for statsborgerprøven (the Norwegian citizenship test)?

Statsborgerprøven is available in both bokmål and nynorsk, and you choose which one. Both have an audio version, so you can have the questions read aloud.

What to choose

The one you've read most of. For most people who have learned Norwegian in Norway in recent years, that's bokmål, because most teaching and textbooks use it.

If you've lived somewhere where nynorsk is the main written form, and were taught in nynorsk, there's no reason to switch.

Is one easier?

No. The content is the same, the questions are the same, and the pass mark is the same: 24 correct out of 32 counting questions.

The only real difference is how familiar the word forms are to you. That's exactly why you shouldn't choose based on what you've heard is easier, but on what you actually read fastest.

Audio

Both written forms have audio. That's worth knowing if reading in Norwegian is slower than your understanding, which is quite common. Hearing the question while you read it saves time for many people.

Samfunnskunnskapsprøven (the social studies test) has the same choice

There, bokmål and nynorsk are two of the options among several languages.