The cost of atime is an extra write every time you read something.

Relatime changes this to one atime update per day (by default), low enough that it usually doesn't matter.

However, that update per day may have significant impact when you are using Copy-on-Write filesystems (btrfs, zfs). Each time the atime field is updated you are creating a new metadata block for that file. Old blocks can be reclaimed by the garbage collector (at an extra cost), but not if they exist in some snapshot.

All of this means that if you use btrfs/zfs and have lots of small files and take snapshots at least once per day, there's a noticeable performance difference between relative and noatime.

I've been using noatime everywhere for several years and I've never noticed any downside. This is definitely my recommended solution.