So to start with, I wanted to clear something up: for some reason, some people out there in internet-land seem to think that there's a rivalry, conflict, or animosity between Lords of Olympus and Lords of Gossamer and Shadow and/or their respective authors. There isn't. We're fans of each other's work; I got a complimentary PDF of LoGaS from him, he got a complimentary PDF of LoO from me. We are both avid contributors to the Official Amber, Erick Wujcik and Lords of Olympus Forums (and I'm only not on the official LoGaS forums due to time constraints). We're both people with a long history of personal friendship with Erick Wujcik, and a long history of participation in and commitment to the Amber RPG.
So if you think there's some kind of issue where you have to choose or "side" with one game over the other, don't.
Now, having written Lords of Olympus, and having finally gotten a chance to look through my copy of LoGaS, I thought I should comment some on the relative qualities of both in comparison to each other. Here's what I'd point out:
1) Both of them are similar enough, system-wise, to Amber that material from each can be used in an Amber game, and similar enough to each other that you can do likewise.
2) Both have impressive art and production values; I don't know offhand if the print edition will be full-colour (or one of the versions will be full-colour, in any case), but if it is, then it will certainly be at least on-par with LoO as a beautiful book (of course, I take no credit for LoO's visual beauty).
3) Both feature new settings, and those settings are familiar in the sense of having to do with powerful groups of individuals capable of crossing through multiple parallel universes.
4) One big difference in that regard is that the setting for LoGaS is completely original, whereas LoO's setting is drawn from Greek Mythology. In the former, you have a set of totally new characters as the powerful NPCs; in the latter, you have the greek gods (pretty much all of them, its a very detailed and thorough list).
This doesn't make one game better than the other, but it certainly makes them different. LoGaS, in its originality, has a group of characters that come with no literary "baggage" the way the Greek Gods do (or indeed, the Elder Amberites did); you are free to do what you like with them without worrying about being true to any canon (except for what the author chose for the setting itself, but which no one will have any pre-ordained affinity or lack-thereof for). On the other hand, the NPCs in LoO come with a ton of mythological gravitas that almost everyone playing the game will be at least slightly familiar with by virtue of cultural osmosis if nothing else. For some GMs, the former will be more appealing, for others, the latter.
So in one sense, LoGaS stays closer to the connection to Amber in its setting-makeup; in another sense, LoO makes use of a pre-existing setting-context that players are likely (even more likely than the Chronicles of Amber) to be familiar with even before getting into the game.
5) System-wise both games have some new material to offer. In general, however, and while its true that as I mentioned above both games stay close enough to the original Diceless game to make them functional together, LoGaS is a lot more similar to Amber mechanically. LoO has more variation, more alternatives and optional rules, and provides more definitions and frameworks to its rules than LoGaS does. Neither are by any means cut-and-paste types of "clones" of Amber, but if what you're looking for is a game that is more strictly cleaving to the line of the Amber rules then LoGaS is definitely your choice. If, on the other hand, what you're looking for is something that presents new rules and new structure and a slightly different framework while still being very much in the same area, then LoO is closer to that.
There's a lot more to say on this subject, but unfortunately its late, and I'm going to be running DCC in just a few hours. So I think I'll leave it here for now; I'd love to hear your thoughts about both games, and maybe I'll write more about this in the future.
Currently Smoking: Lorenzetti Tempesta Apple + Argento Latakia