I'm not sure if there is any real answer to this question without more details, but I'll give it a shot anyway, since I think it's an interesting question.
Here are some things to consider when choosing which should be more prominent:
- Which part (the logo or the text) is more memorable? The more memorable one should probably be placed first.
- Which one is used in other branding associated with your company? If you've been handing out business cards and letters with only the company name, you might want to put that first so that your customers associate the new material with your company.
- Which part conveys your message? If your company name is Joe's Coffee Mugs and your logo is an abstract shape, then your company name should be more prominent because it conveys your message. If your name is Albertson's but your logo is a coffee mug, then the coffee mug should go first, because it does a better job of conveying what your company is about.
Once you decide which should be more prominent, that one should most likely go on the left, however that is not necessarily the case. You should also consider the alignment. A logo placed partially into the right margin might be more noticeable than one that was on the inside but right-aligned.
I'm assuming this isn't the case with your logo, however it is also worth considering if there is a natural flow of logo to name or name to logo. If you logo has a green to red gradient and your logo is red, then the logo will look more natural on the right.