Greater Trip (unlike the D&D 3.5e version of Improved Trip that it’s partially based on) is ambiguous as to its timing: it says the target provokes an attack of opportunity when you successfully trip, but since attacks of opportunity usually interrupt the provoking action, that might mean that you AoO them while they’re still standing.
We can reject that possibility, however, on the ground that it could result in an arbitrary number of attacks: since the target is not prone, you can trip them again, provoking more AoOs. Since you are tripping and not attacking, this would be pointless—unless you have nearby allies with Combat Reflexes who can benefit.
Clearly, that is not a good thing to introduce to the game. We thus rule that the AoO occurs after the target is prone. That resolves the question regarding Landing Roll: since that occurs before falling prone, and Greater Trip’s AoO happens after, Landing Roll must occur first (and thus can potentially allow the target to avoid the AoO).
Riptide Attack is much more ambiguous. There is no clear ordering here, and furthermore it’s not clear that, after you have used one or the other, you are still eligible to use whichever you didn’t use immediately after the trip. It seems unconscionable to me that Paizo didn’t explicitly clarify this situation, when Greater Trip and Riptide Attack share so many prerequisites and are obviously going to be considered together.
As for ruling, you should allow them to both be used, in whichever order the tripper likes; it’s a minor thing, really, but Pathfinder melee types need an the help they can get.
