I can say something on the Iliad side:
Sweet spot(s): It handles AJAX painlessly. For me, that was the turning point that made me switch to Iliad. Also, it's so small and non-bloated that you can read the whole code in a day and have a grasp on how it works.
Weaknesses: The community is also very small. This results in a lack of documentation, additional modules or pre-made widgets. OTOH, small communities tend to be willing to help each other more eagerly, so pretty much all your doubts can be solved by asking at the mailing list.
URLs: Well, since all calls in Iliad are AJAX by default, the URL stays clean the whole time.
Ajax: Yep. For free and by default. You just #markDirty a widget and it'll update automatically. Dependencies are as easy to define as sending #addDependantWidget: to a widget, so that when the first is marked dirty, both will be updated. Also, if the client doesn't have a javascript capable browser, all calls will fall back to regular HTTP requests automatically.
Persistence: No preference. Since the model is separated from the framework (I think this applies for the three frameworks) you can still follow the same guidelines you would for Aida or Seaside.