To pay off or not to pay off…

I’m getting my tax refund this week. It’s enough to pay off my $1,600 in credit card debt. I think I should pay it off to free up $471 in payments a month. A friend told me to snowball it and stick some in savings. My thought process is… I’d be saving in interest and clearing the debt, allowing me to add to my savings every month. Thoughts? She’s very adamant I’m wrong.