While padded shorts without shoulder straps do work okay for cycling, we always prefer to ride in bib shorts for several reasons. Traditional shorts without straps typically have an elastic waistband to keep them snug around the waist and prevent them from slipping down. While somewhat effective, the tension on the waist can press on the abdomen, especially when in the forward riding position, which can be quite uncomfortable. Additionally, regular shorts usually start to slip down or sag after a while which can reveal some of the lower back and/or allow the pad to move out of its optimal position.
Overall, we feel that bib shorts are far more comfortable. The straps that hold the shorts up negate the need for a tight waistband and help to keep the shorts in the right position without any unwanted pressure on the lower abdomen. When articulated forward in the riding position, the straps keep the shorts from sagging while holding the seat pad in the correct position regardless of how you move around on the bike.