The things that make for a nice running shoe are bad for bicycling and vice-versa.

For running you want a nice flexible sole and cushion is good.
For bicycling stiff soles rule and thinner is better.

My experience is the longer distances that you ride the more you will appreciate clipless pedals. I use SPD flip-flop pedals on my beater. If I'm planning to ride more than a few miles I'll take the time to change into my SPD shoes. If I'm just making a quick run up to the hardware store I don't worry about what shoes I happen to have on.