Flame is similar to Apo (though has a whole bunch of extra capabilities, some of which are only now starting to be implemented in Apo, such as 3D flames)
Prime is kind of similar to UF but designed from the ground up to be extensible in small chunks (instead of just "transform", "formula", "colorer", there are literally dozens of different kinds of objects that can replaced/used with others - everything from full renderers down to little objects that simply adjust a value). For example, in UF anything that wants to make a colorer that is based on using traps has to re-implement all the different traps that they want. In prime, traps are just another kind of object (which can be derived from "anything that can measure"), so if you want to write a colorer that uses traps, you get all the traps installed (and any other traps others come up with). Plus the use of inheritance allows you to make a bunch of similar things using a common ancestor, and there is also a wider range of basic data type (for example, you can have a "expression" in the UI that allows the user to type in a formula, as well as UI items for gradient parameters, curves, and images).