I believe that what counts is your finished product.I have seen people try both methods and some who claim to only use a roller.I have had the best luck cutting in first and rolling second.

I agree with Matches. Don't let the "cut in" part dry before doing the other painting. Keep a "wet edge" so the cut in part won't show when all is done.

Cut first, then roll as close the edge as possible. This way you minimize the brush strokes on the finished wall.

As for keeping a wet edge: that's critical when using oil-based paints. Not an issue with quality latex paints.

Another hint: mix all the gallons together before starting. There will be shade differences between gallons of the same color and mixing together eliminates this.

I always learned that you cut (do the outer rim) first, then roll so that you get as much of a rolled finish as possible: namely, so your roller strokes go over the brushstrokes as opposed to your brushstrokes going over your rolled strokes.

Also, as others suggested and as th Hometime page recommends, you should not "cut" the entire room at one time, but instead just do manageable protions first so that the paint does not dry before you roll over it.