I certainly understand your dilemma. If you are a one-person business it is very difficult to write in third person unless your aim is to make your reader believe that you have a larger team than you really have. Still, you don't want to make your site look like it's all about "I".
I generally try to go for more personal so that the person reading realizes that there is a person at the other end of his/her computer. However, personal has little to do with either "I" or "he". Personal has to do with "you". Get your reader involved in your writing by using active verbs and showing him that there is a person at the other end of his/her computer.
If you are showing case studies in your portfolio, then start with "Company XYZ" needed (blah, blah, blah). Then you are fine to say "We were able to find a solution to their problem through...." because you are talking about you and your client working together.
Another example is to show your clients what they can depend on from your company. There, I think third person works well.
"You get a professional (writer, developer, designer) with XX years of experience."
It's also okay to throw in a little first person "Original articles are my specialty."
As said before, it doesn't really matter third or first person as long as you write so that your reader understands there is a person at the helm of your business. Even more important is that you show your reader that you understand there is a person at the helm of their business.