Ive played a decent amount of Saga, though only the viking age factions, but I own C&C. Ive also played a good amount of Lion rampant. Both are fun and have their respective shortcomings. Lion rampant is very fast paced but is a very fickle game, a players turn can end without moving a unit, which is both frustrating and fun, but it adds a fun random element to the game. Lion rampant's strength is that all the unit types play the way they should. Saga is fun, and the battleboard's give all the factions their own flare and flavor. In my opinion, the shortcomings of saga are the scenarios, but thats not the end of the world, and im sure some may disagree. Lion rampant comes with twelve scenarios and they're all pretty fun. Saga just came out with a campaign system called age of the wolf (or something like that), and all the saga factions from C&C and viking age are theoretically compatible to play against each other and are balanced. The shortcomings of Lion rampant are that armies can be rather cookie cutter/ similar, but that depends on the type of armies you create. In lion rampant the lists are just guides and are not strict for army construction, you can build whatever army composition you want with very little limitations. The idea in lion rampant is to have little restrictions and to really make a force that seems suitable to the time/theatre of battle.
I mainly game the baltic crusades, from which the Teutonic Order got their fame. For Saga, the Normans are suitable as the teutonic order, as are the Franks, and all of the christian factions in C&C are suitable as well. Saga Rules cost a bit more than lion rampant. Another suggestion if you decide on Lion rampant is to buy the fantasy version dragon rampant, they are exactly the same, but dragon rampant offers a little more unit cusomization/upgrades. Fireforge is about to release their medieval skirmish rules in a month or so, but I have no information on its mechanics.
So in short, saga factions have more variety in their play, and Lion rampant variety is a little more limited, but its ultimately up to the players in Lion rampant. Both are fun. For saga, I use normal d6 for the saga dice (boo, hiss) its a really simple conversion. Lion rampant may be a little faster paced because of the fickle nature of the turn structure. Check out my blog to look at my baltic crusades minis, I have some halfway decent lion rampant battle reports, and some really poor saga battle reports.