Proof? I used an AOL email for my Battle.net login for years and never had either account hacked (while some people with Blizzard authenticators got their WoW accounts hacked). I never got 1/10 the random spam in that account I did with Hotmail or Yahoo! accounts (granted, I only used it for my WoW login) and it seems to have all the usual security features any free email would.
Proof:AOL doesn't use SSL encryption. Spam has nothing to do with security, and even to a degree has little to do with how public your email address is, but rather has to do with how coherent your email address is (Yahoo!, though, isn't much better than AOL for also not giving you SSL encryption). Incidently, though, Yahoo! has the worst spam filter out of all the major email providers (Hotmail used to have a horrible one, but was significantly improved with the introduction of Windows Live).
As far as security features are concerned: Gmail and Windows Live are leaps and bounds better than AOL and Yahoo! There's literally no comparison between the two because the gap is so huge. (one-time passwords, two-factor authentication, log-in tracking, SSL encryption, computer-locked login, etc)
As for the other: http://dailyworth.com/posts/784-Want-a-New-Job-Ditch-That-Old-Email-. Basically, AOL and Yahoo in particular (As well as Hotmail, though @live.com not so much) make you look old and tech-illiterate. You'll find various articles on this matter all over the place quoting various job interviewers and HR employers (that was just the first one i found in a quick google search).