First of all, your developer should have recommended you a solution. If he didn't, he is probably trying to impress you. Also, unless it is a company with more than 5 coders, do not hire this coder. It is impossible to be specialized in all those platforms. He might know all of them, but he is average at best. CodeIgniter & WordPress are "smaller" and easier/faster to learn but Drupal for example is HUGE and very very complex!
Second, him asking you what you prefer is kinda stupid because each of those platforms is suitable for different purposes and situations and development time and cost varies considerably. A WordPress site could cost $200 to develop, a Drupal site could cost $1000.
CodeIgniter & Zend - for custom coded sites
Unless the developer is a newbie or retarded you get best performance (10-40 times faster than the other CMS') and best flexibility - since it is custom coded from scratch you have no limitations. On the down side, if you need something added to the site in the future, you have to hire a coder to create it because you don't have plugins or stuff like that, or even a community behind. For site that are not pure CMS' or difficult to build on top of a CMS, this is the way to go.
WordPress - if you want a blog or a relatively simple site
For anything other than a blog, magazine-style site or a site built around articles, I do NOT recommend WordPress. WordPress is NOT a CMS. It is a blog platform. It can be customized to behave to a certain extent like a CMS but it is a piece of crap, poorly designed, poorly architected and poorly developed. Compared to Drupal or even Joomla, WordPress is like a retarded guy in a mental institution compared to a Nobel prize winner. I don't give a rats ass how popular it is or how many people like it here. It is a piece of crap (yes I do use it myself but I am aware of all it's problems and I don't need something more complex than it can handle). It has major SEO-related issues, usability issues, huge performance issues if you run a big site (a lot of content or complex content types) on it, etc. Also it is very difficult to customize in certain areas. On the good site it is very simple to use because it is just a blog platform. You have lots of plugins you can install yourself (though most are just as crappy as WP itself). Development and customizations are cheapest for WordPress from all CMS'.
Drupal & Joomla - serious CMS platforms for serious sites
Drupal is the best CMS platform out there. By far! It offers unparalleled flexibility and an exceptional architecture. Joomla is close, but not really that well architected or implemented (still a lot better than WordPress). However, development of a custom Drupal or Joomla site is much more expensive and much more complex. As a matter of fact, while Joomla could be used just with a theme and some plugins out of the box, I think Drupal should never be consider unless you plan to customize it a lot (custom coding). Joomla is relatively easy to manage, Drupal is very difficult to manage (has a gazillion of options and settings and you will feel overwhelmed the first time you login into the admin area). However, if you build a big, complex site like MTV, White House, NASA, Packt Publishing, etc. Drupal is the best choice. One other aspect about Drupal is that it is not recommended to run a Drupal site on shared hosting but on a dedicated server or at least a VPS so that you can fine tune the server for Drupal (more money to spend on this).
Magento - pure online store
Magento is a shopping cart platform. Possibly the best shopping cart platform but far from the best CMS if you plan to build a site around articles/news/etc. For example if you want a pure store, go with Magento. You cans till have normal "article" pages but it is not built to be very flexible or potent in that area. Again, this dude that asked you what platform to use should be fired. Why would he suggest Magento and Drupal/WordPress/Joomla in the same sentence for the same project. If you need an article/content-oriented site with a shopping cart, then Drupal has Uber Cart project which is perfect for that (almost as good as Magento itself, certainly as good with heavy customization). Magento is not very expensive to develop on because normally all you need is a theme. If you need massive customization and feature additions to Magento, then Magento is not the platform you want.
Giving you a comprehensive answer and comparison between all those platforms would require me to write at least 10 pages. It is actually easier if you just tell me what kind of site you need, what features it should have and about 5 sites that look and have the functionality you need. Then I can suggest you the best approach.
Again, you should seriously consider not hiring this developer, that is the first piece of advice I can give you.
