What do you think is more important or makes the bigger impact: the résumé or the cover letter?

Both are equally important for different reasons. Employers absolutely read both with a fine tooth comb. Spelling errors are the first thing, as well as grammatical errors. Make sure they are perfect. Next, they want to see an interesting career path with applicable skills and training for the position you are applying for.

The cover letter should highlight things about you that the resume may hint at, but the letter is your place to shine and make them notice you.