You rarely have to do both at the same time. IMHO if you've just started out on a startup - its better to be a designer because you can do customer devleopment

You rarely have to do both at the same time. IMHO if you've just started out on a startup - its better to be a designer because you can do customer devleopment without touching a line of code but by having a design which shows the customer exactly what to expect. After you get a bunch of people begging you to build, then you build.