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.

I think in this day and age of computer-based application and hiring, both are losing their importance...

I know at our hospital, all applications are online, and you cannot "attach" things, only cut-and-paste into designated boxes, so all of the time-consuming work designing and printing out beautiful resumaes and cover letters is for naught...

That being said, proper grammer and spelling is important even in the world of cut-and-paste...

Yes, online apps are common, but my latest online app still wanted a resume and cover letter cut and pasted into the fields on the app. Better to learn how to do a really good letter, and follow up any interview with a thorough and thoughtful thank you letter.

Both serve a important role.. you have to consider what the position is that you are applying to..
The first time I was ever asked to write a cover letter I almost died... I had always had a resume but never a cover letter.. I actually missed the deadline of the position because I was terrified of writing that cover letter... I mean come on,,, how do you write a letter that boast of your best features without sounding conceded?????? It really makes you take a long look at what you think of yourself and what your self worth is.... That first cover letter was written hmmm prob close to 10 yrs ago... however I will tell you this.. once it was written I have used it over and over and over again... now all I do is copy and paste it and tweak a line or two here and that that customizes it to the job in which I am applying for...

Yes, cover letters are crucial. What is often just as important---or moreso---is the letter you write to a potential employer after your first interview. In that thank you letter, you highlight what you are excited about, and you highlight again what skills you can bring to the position. You can also reflect on the organization or facility and offer some praise about what you have discovered. And of course, you thank your interviewers for their time and interest......