The additional inks are part of it, but there's also the matter of drop sizing, drop positioning and dithering algorithms. A photo-oriented printer will produce text and business-type graphics that are a little less crisp than they can be, and long, smooth, pure gradients often pick up a bit of banding†, while a text-and-graphics printer tends to add subtle artifacts to photographic images by finding and enhancing what it perceives to be edges -- an effect not unlike oversharpening.

If the most important aspect of your printing is going to be photographs, then go with a photo printer -- its text output won't be all that bad. You'd notice a difference in a side-by-side comparison with an equivalent-level text-and-graphics printer on a top-quality hard-finished paper, but you wouldn't notice anything deficient on its own at font sizes greater than about 6 points. (Long gradients in printed PowerPoint slides might not be perfect -- but printed PP slides are not the intended end product unless you're stuck with an old overhead projector, and they have enough optical problems that nobody would ever be the wiser.) You will, however, notice that your photos won't be nearly as good as they might be if you use a general-purpose printer, even if you can't quite put your finger on why.

† Real photographic images rarely have long, smooth, pure gradients; there's almost always some amount of noise even in, say, a blue sky to add a degree of "natural dithering".