Do you really know the difference between Citi Bank and Citibank? No? Then EV hasn't saved you from being phished.
Section 9.2.1 (Page 9): https://cabforum.org/wp-content/uploads/EV-V1_5_7.pdf
In addition to using & verifying the legally registered name, it must be verified that there is a physical address for the business, if that address doesn't match the registered location, additional verification is required. There are additional provisions of verification as well. See section 11 of the same document.
I don't know if it's worth the money per se, but you can pin a couple of trusted CA root EV certs via HPKP and know it's much more difficult for someone to "accidentally" issue a valid cert for your site.
If you do that, users won't see a lock instead of a green bar, they'll be blocked from accessing the site at all (if it's not their first visit and they're using a modern browser).
The only security feature EV certs have over regular ones right now is the use of certificate transparency, but that should be extended to non-EV certs within 1-2 years.
You could pin your own cert, but that makes it difficult to rotate keys in a heartbleed type situation.
Though it would not protect from factoring because most EV roots are the same key length/hash.
For anyone else reading, this works because the root programs give authority to issue EV certs separately from other certs. To keep the authority separate (most, perhaps all) CAs use separate roots for EVs.