The answer to this question is pretty simple: both.

Flat design illustration is something that was picked up really fast by designers, especially to design flat iconography, thus achieving a very interesting effect using flat colors on these icons. These illustrations look great and are really a good complement to the flat look on your website (if they are indeed relevant to your product and target), but photos can (and should) also be used. Flat is not only about text and simple colors; it's about creating a layout where your photos and your content stands out, by bringing the focus of the user on the content instead of on the interface. This was something that often happened on skeuomorphic interfaces.

Nowadays, it's very common to see websites using very wide and high-resolution photos of people, products, or environment to showcase their product in a real-life situation more easily. It is frequently said that a picture is worth a thousand words, so, use those pictures...