Back when I was fiddling with Eclipse RCP development one of the things which frustrated me about SWT in Gtk+ was autocomplete behaviour of drop-down lists. Type-ahead doesn't work, so while you can use the arrow keys to move through the list, and hit space or alt-down to see the choices, you can't hit keys and have the right entry show up. It works fine in Windows, so I'd presumed it had something to do with Gtk+.
I think I was right, since I've run into this again with wxWidgets in Gnome. I went as far as trying out some more widely used wxWidgets apps, and they all have the same problem, so I have to assume it's not just me doing something stupid. I found some wxPython code which tries to implement type-ahead on list controls but frankly, it's all just a pain in the butt. I went as far as trying out a simple combo using Gtk# in MonoDevelop, and it's the same thing.
Given my dislike of Swing, I have to grudgingly admit that I tried it in Swing, and a JComboBox does exactly what I expect.
Update: I noticed GtkEntryCompletion which seems to do the trick, but it doesn't seem to be exposed via wxWidgets.