Computer generated text has sharp and smooth edges because the pixels at the edges have a computed opacity. This is (abusively) called "anti-aliasing".

If you put the text in your photo, it becomes a bunch of pixels and its size will change if the photo is scaled for printing (which is often the case). Scaling a image is done by interpolating pixels (i.e., a pixel in the result is a "blend" of pixels around its corresponding position in the source). The scaling algorithm doesn't know that the edge pixels are anti-aliasing pixels and applies the same interpolation algorithm than on the image.

Interpolation always introduces a slight blur so the text can become blurry. The image can be sharpened to eliminate the blur bu the high-contrast edges of text will often "over-react" and show artifacts. So, either way, the text edges are no longer smooth and clean and our eyes are rather good at noticing this.

By contrast, if the text is kept separate from the image, it can be kept as text data, and rendered at the final size after the image has been scaled for printing, so its edges are not subject to degradation. In some printing processes they could even use techniques similar to sub-pixel rendering.

So in theory keeping the text separate can give better results. But that could depend on the actual print process, and maybe the edge degradation can be lived with anyway.