Email confirmation and CAPTCHA solves different problems. The first one should be implemented when you want users to use their real e-mail address in the registration process. Email confirmation also protects us from identity theft. I cannot register by typed the whitehouse.gov emails address and pretend that I am the President ('cos I'm not able to click on the confirmation link sent to whitehouse.gov, because I'm not the owner of this address). So email confirmation allows to link each user to each email address.
However email confirmation doesn't protect us from the bots (as the CAPTCHA does). Honestly, almost every spam-bot I've seen had email confirmation implemented. It's really easy stuff and it's just a few lines of code to force our program to check emails and click on every activation links). The interesting detail is that some of that spam-bots used 123456 as the password to their webmails accounts.
So, let's talk about the CAPTCHA. It was created to distinguish human from the robot. Reading the text from the image, solve maths formulas, etc. The main problem is that online robots are still evolving. Their modules are upgrading, they haven't got problems with solving formulas, their OCR modules are better (so they are able to extract text from the image). All of these means that CAPTCHA is not the 100% protection against non-humans, but it's the first defense-line and it's very recommended.
The best CAPTCHA is the CAPTCHA which was implemented by you. Trust me, a lot of people try their luck with breaking popular CAPTCHA. Why? The answer is very easy here. Popular CAPTCHAS are used by a lot of website. If we can break that CAPTCHA, then we could put a lot of spam content on that websites. So if your website is not very popular and has own CAPTCHA implementation, I am pretty sure, that noone will lose their time and money to break your CAPTCHA. However if you are not sure how to implement it in the proper way, you could try non-obvious CAPTCHAs. Like image-base CAPTCHA (here is the example) or 3D CAPTCHA (another example).