Hi... I do both. Quilts for play and drag-around are done by machine these days, which includes those that go into the community to meet needs for coverings. Sew binding to the back, roll to the front and machine stitch with your choice of finish .. I DO cut that binding at 2.50 inches so I don't have to tug and miss while stitching.
Some prefer bias cut binding, but according to some of the 'experts' that is not necessary unless you have curved edges. I tried doing that, but found I pulled too tight, and my hard work was all for nought as it looked sort of messy. I tried to reason out the difference, and all I can see playing with the fabric is that on the bias puts a bit more strain on the threads as they are pulled crosswise .. so ... I just stick with diagonally sewn strips cut straight from width of fabric.
BTW - I very rarely cut borders from full length (parallel to selvedfe) ... I have yet to m ake one so wide or so long that it actually stretched out of shape .. and .. if concerned .. a basting stich around the outside edge of the quilt before the next steps is a lot cheaper. IF it is important to get a certain pattern - there are always exceptions of course.