> Is there any downside to registering a Facebook page custom URL or
> Google plus custom URL?

No, this will help users more readily identify links and increase their likelihood of clicking on them.

> Is there a risk of these social media custom URLs competing with my
> own domain's website and cannibalizing my own traffic?

Not likely, the domain would still be `facebook.com` or `plus.google.com` so content would be indexed under those sites, not `www.example.com`. This is not any different than having a user string instead of a custom URL, and that's typically not an issue with those either. Unless you have a large amount of [duplicate content][1] on both these social sites and your site, there wouldn't be any cause for concern.

> Or do the benefits outweigh the risks?

There really aren't any risks, it's just a different URL structure that's more easily recognized and remembered by users.


  [1]: https://support.google.com/webmasters/answer/66359?hl=en