Great web design is really about personality. Getting to the root of the client's brand, reflecting both their position and nature effectively, and making each element work in harmony to send the same strong message to any visitor: this is who we are, and why you should care.
With today's wide range of options in web design (both in terms of technology and personnel) there really are no obstacles to having a great website other than bad decision-making. While budget certainly plays a key role, and there is a wide range of expertise between web designers and design firms – the client needs to understand themselves well enough to provide good direction, or step back and let the design team refine their brand and present it in its best light. A great web design team will be very well suited to doing just that – and having the perspective of someone who doesn’t live with the client's brand every day, and having been presented with similar problems before (and the experience gained from solving those problems) really lets them see what speaks to the client's audience, what are the key points to focus on, and ultimately the best way to present that information.
There are many other factors that go into the process, but it comes down to smart, strategic thinking first – and great design execution second. Deciding on the best web design firm for your company should start with the best web design conversation.