I first started using Traits and TraitsUI to build GUI's as a postdoc researcher in Mechanical Engineering. My previous experience with building GUI's was with MATLAB's GUIDE, and I found TraitsUI to be very straightforward and easy to get started with by comparison. TraitsUI has a very linear progression of progress versus effort, and for the limited amount of GUI building I did with it, it was more than sufficient.
As a professional developer (full disclosure: I work at Enthought), my perspective has shifted somewhat. First, it is important to make the distinction between Traits (the typing, validation, notification, and dependency system) and TraitsUI (the GUI layer built into and based on Traits). I use Traits all the time, and it undergirds a lot of the code I write. Particularly for its dependency and notification utilities, I consider it to be invaluable.
It doesn't take too long, however, to start bumping into the limitations of TraitsUI for application building. As I mentioned before, TraitsUI is sufficient for small- to mid-sized applications, but it gets difficult to create more-complex layouts, and we were spending a lot of time wrestling with TraitsUI to produce larger, more involved and flexible application interfaces.
That led to the more-or-less blank-slate development of Enaml. Enaml uses a constraints-based layout system at its core and integrates with Traits. From the outset, it addresses the layout weaknesses of TraitsUI. Every one of us that has used both systems prefers Enaml, and we consider it the tool of choice for GUI-building moving forward. The level of control and flexibility to lay out GUI's is remarkable --there are some nifty demos to check out in the repo.
That said, there is a slightly (but only slightly) steeper initial learning curve since it is helpful to have a grasp of certain concepts such as MVC separation from the outset. An experienced developer would see the value in this right away, but it might be more of a hurdle for a new user with a science or engineering background. It is only a slight hurdle, though, and easily cleared. Also, while the feature set is nearly complete, there are still a few holes. There is steady progress on filling them in, but Enaml is technically still in beta.
Overall, if you are trying to decide which tool set to learn, my recommendation is to learn Enaml. It's what we are and will be using going forward.
[UPDATE - Jan 2018]
Since this answer continues to get views and generate conversations, an update on this opinion is long-since overdue, the first answer dating from late 2012. Enaml has largely been the work of one main developer. When he left Enthought in early 2013, he forked the enaml repository and started developing it in the nucleic/enaml repository. We (Enthought) decided not to develop a competing fork and introduced a thin interface library enthought/traits-enaml to provide ongoing compatibility with changes in nucleic/enaml
. Around the same time, we also introduced enthought/qt_binder to provide easy access to low-level Qt widgets in the Traits/TraitsUI framework which provided much of the same kind of layout flexibility that Enaml provided.
Now Traits/TraitsUI is the stack we use for most application GUI building. We continue to maintain and develop Traits, TraitsUI, and the other libraries in the Enthought Tool Suite (Chaco, Kiva, Envisage, etc) in Python 2 and 3, and they continue to meet our needs, especially in the enthought/envisage pluggable-application framework.
My amended recommendation is if you want to build a rich-client application (not a web app, that is) in Python, I would say to learn Traits and TraitsUI.