I think anyone using Social media, or similar, is vulnerable the second they start to broadcast their life into the world.
In terms of a security risk, only really as far as you assisting the bad guys with the Social Engineering part of their attack. Yes, you'd probably be easier to find across multiple platforms, but there a lot of variations.
It'd depend on what profile picture is in use, if it's of your favorite Ferrari, there is a very high chance your favorite car picture is also thousands of other peoples favorite Ferrari. Returning that on a Google image search when trying to find someone called "John Fakename" would be difficult. There may well be many other "John Fakename" out there with the same car picture.
If however, the profile picture in question is of you standing in front of your TV at home holding your best animal friend, a Google image search on that (on the assumption this image is on other accounts) would presumably only return YOUR profiles, and not other randoms with the same name. It'd be much easier for any attacker to say "Ha! There! that's the guy I want" if the same pictures are used.
It's not like using the same image would pose a large enough threat for me to suggest you not do this.
With regards to what should be taken into account when choosing a profile picture, it depends how security conscious you are. There is really nothing more to it, if you'd rather not be easy to locate across multiple platforms, change it up, if you don't care, don't.
Your face picture makes you easily identifiable, remember this. If you're using Websites that don't require face pictures, yeah, i'd avoid it, but that's just personal choice.