The advantage of marking first instead of trimming first is that it is much easier to sew an exact 1/4" seam without any stretching or slippage. It allows pinning to the right of the sewing, for example, to keep everything aligned. Also, it allows you to increase the amount of batting that fills the binding, if necessary.
This is a technique I developed for myself after a particularly difficult quilt, where the edges seemed really hard to control.