The Ultimaker 1 (or Ultimaker Original as it’s now called) is the first model that was released back in 2011, and was based upon a prototyping workshop project. As such, it arrives as a kit of parts that you put together yourself, the build time for it is around 10 hours (though a team from a school in Lancashire built one in 4.5 hours recently in a competition to see who could build one in the quickest time). The Ultimaker Original has a lot of 3D printing enthusiasts using it, and they design improvements and upgrades that you can print out to use on your own machine. It has a unique appearance that shows how it came from a prototyping background.
The Ultimaker 2 (launched in 2013) is a very clean, consumer-oriented design that looks great and arrives fully assembled and ready to print. It also has a heated buildplate (which the Original doesn’t have – though you can buy an upgrade kit to add it on), this is something that you need if you are going to print using certain materials. The Ultimaker 2 is also not as modifiable as the Original.
There’s quite a difference in price, so which one you choose depends mainly on your budget, and whether you want to learn about how the printer works by building one yourself or just want to get printing.