Interesting thread. I'd love to actually see the design to weigh in. I would go with the more creative/whimsical one, but that's based on what I chose to do with my business.

I'm in a very "professional" profession (law), but went fairly lighthearted in terms of both my logo and my website, which reflects the logo. Most people who do my job (private judge and mediator) have terribly boring websites with a horrible picture of themselves. And the written content is generally just their CV/resume. I worked with a (cyclist) friend and he came up with a fun visual website that is VERY different from others in my field. I don't get a lot of business "from" the website - no one in my field does. (It's all word of mouth and referrals). But I like to think I'm providing something that shows a sense of creativity when people are evaluating whether to use me. Creativity is critical in what I do.

Here's mine:
http://www.BurkeADR.com

Would love to see yours when you have something on paper.