Looking for a non-D&D high fantasy roleplaying system

[Shingen]

I've really enjoyed Legends of Anglerre, as it is a pretty good fate ruleset for it.

Storyteller doesn't necessarily have fantasy, but Sorcerer's Crusade and the Dark Ages line both could provide reasonable simulacra.

 

[RobShanti]

I have to second the Ars Magica recommendation, but with two caveats: it's great for a game centered around Wizards, like World of Darkness's Mage game (which is Ars's intention), but not so great for other character archetypes. It definitely has the best magic system I've ever seen. The other caveat is that I'm speaking about 4th edition Ars Magica...I've never played 5th edition.

Some of the FATE based systems might work, especially Strands of FATE. I may not be evolved enough to hand over too much narrative control to my players though.

I also recommend FATE. I'm running a game set in Tolkien's Second Age using, of all versions of FATE, the Spirit of the Century (30s pulp) rules with little to no modifications for a fantasy setting. It works great, and frankly, you don't really need to turn over that much control to the players if you don't trust them. It's easy to use FATE with pretty much any GMing style.

 

[Penthau]

I also recommend FATE. I'm running a game set in Tolkien's Second Age using, of all versions of FATE, the Spirit of the Century (30s pulp) rules with little to no modifications for a fantasy setting. It works great, and frankly, you don't really need to turn over that much control to the players if you don't trust them. It's easy to use FATE with pretty much any GMing style.

The systems where I started getting nervous about handing over narrative control was Dungeon World. After some reflection, I discovered what I felt to be the difference between DW and Fate. DW allows consequence and cost free player control of the narrative, but Fate costs at least a little bit to gain control. It was way too easy to get goofy and silly in what was meant to be at least a semi serious DW game.

 

[czipeter]

The systems where I started getting nervous about handing over narrative control was Dungeon World. After some reflection, I discovered what I felt to be the difference between DW and Fate. DW allows consequence and cost free player control of the narrative, but Fate costs at least a little bit to gain control. It was way too easy to get goofy and silly in what was meant to be at least a semi serious DW game.

That's definitely a thing to consider. If you want to run your game, than giving away so much of your power is not the way to go. A Dungeon World session would suffer a lot under that assumption. DW is much more easy on what a certain player is allowed and required to say. (OTOH, DW is much more picky about the "when?". You don't get to say those things all the time nor are you required to do so.)

I myself like it much better when I can "co-play" and "co-run" the game with the other participants, so it's more than OK for me if their ideas are not being read from my mind / my world description book. This way the tone and genre of the game will be a group product. If someone is having funny ideas, another player serious ones, then the end product will be a bit ambiguous. That can be a good kind of ambiguous if they were paying attention to each other's tone.
My goal in gaming would be much harder to achieve with FATE where everybody has to "pay" for some of their ideas to be included--which is an incentive not to have these ideas at the first place. It requres you to pay for it but you can still do it--a weird kind of middle way to go, if you ask me.