Can someone tell me what's the difference between Cocoa and Carbon? I want to download Eclipse but I don't know which one to pick, I have option to choose Cocoa or Carbon.
Cocoa supports features like spell checking and 64-bit right out of the box. Carbon is looking increasingly frowned upon by Apple. Cocoa is the way forward.
(Note that Carbon is still widely used for lower-level stuff. Many Cocoa applications dip into Carbon from time to time, and a lot of Cocoa is built on Carbon. But if you want lots of yummy UI goodness for free in each new OS, you want Cocoa.)
A basic answer would be that they use different "wrappers" around Eclipse in order to interact with the host operating system.
There is a version of SWT (the GUI toolkit used by Eclipse) that works with Carbon, and a version that works with Cocoa - so your choice isn't so much a choice of versions of Eclipse as it is a choice of which version of SWT you prefer.
The advantages of Carbon are that it's faster and more mature so technically it should be more stable. However Carbon has been more or less EOL'd with Apple's plan to not transition it to 64-bit and have developers move to use their Cocoa API instead.
The advantages of Cocoa is better integration and free extra features that are available around the operating system (eg. spell checking, various shortcuts in Open/Save dialogs), better Spaces support, etc.) Additionally you can use the 64-bit version if you'd like but it will require a 64-bit processor (which if you have an Intel Mac you're nearly guaranteed to have - only a few models shipped with 32-bit processors)