
The reality is that web designing is a completely separate field of designing, having its own flare and expertise. These are two different mediums and so the target audience and objectives of a websites are entirely different from a piece of graphic design. There is always the possibility that a graphic designers advances to the level of a web designer once
he learns certain technical skills, but it's important not to assume that a rockstar graphic designer will instantly be successful when designing for the web.
So when don't assume the shomolu guy who did your flyer design can also design your website. Get a professional website design company to do that.