One is not better than the other, they are simply different approaches to achieve similar goals.
It sounds like what your client is really saying is that they want the column headings to stand out from the content more. One of your jobs as a designer is do interpret what your client wants into a visually appealing design. So try some variations on what could make it stand out.
Things that you can vary include: font type, font size, font colour, font weighting, alignment, background colour, background texture, padding, cell height, cell border, border colour, border weight and letter spacing. Those are a lot of options, and you can't expect your client to understand them all and the visual consequences of them.
You should still do a version with exactly what your client asked, but you should also present one or two versions of your own that try to achieve the same underlying goal. You should also explain why you believe they are better, but use objective terms rather than just saying "I prefer this".
After that, if your client chooses something you don't like, it's up to you whether to accept it, quit, or fight for your choice. And that is a wisdom issue, not a UX one :)