Well, I'm not very fashionista, and should say:
- If you want the visitors to click on them, they have to be clearly different from other images on the page (the pure illustrations or design things).
- Traditionally a link was an underline text or a UI-button. Visitors are used that clickable items associate to that, and expect that they are more or less buttonlike: 3d.
- A 3d suggestion can be made by a bevel, or a (subtle) border with some shadow: then the visor knows the (important) area where to hover/click. That is is recognizable, user-friendly, and more calling to action!
- Besides a sort of 3d (if the rest is flat), the difference with other images could be also: an introduction text line ("Here you can find our activities: "), the position on the page, a different background color, a different border, a different shape, a different ...
Personally, I don't like "just flat images" too much (with some exceptions for common known logos or icons like Facebook, LinkedIn and so).
But as always: "what is the best, is depending of the rest", the context of the design of the whole page!