Epic's engine can be used for creating outdoor areas, but as I said, the engine is tailored more towards indoor design above all else. Creating outdoor areas which look as nice as FarCry's, regardless of what other pros the engine has going for it, will be difficult.
Of course, Doom 3 could
become more viable depending on how exactly you plan to go around this mod. If you plan to have the entirety of Blood Island as one huge map, then FarCry is without a doubt what you want simply because it has brilliant handling of LoDs, draw distances, and managing a lot of stuff being rendered on screen at once. The Doom 3 and Source engines, put simply, don't.
This is primarily down to the way that the two engine render things. They do a lot more calculations to ensure that lighting and such is pixel perfect, whilst FarCry sacrifices that to an extent and instead "cheaply" renders huge stretches of terrain without much slowdown. Source can also do this, although you have to use a special type of floor mesh which is called a displacement map. Source does not really use LoDing on anything other than models though, which makes huge areas of visible detail (stand on top of Blood Island volcano, look down) really difficult to do at a satisfactory frame rate. Doom 3 also has this issue, amplified x1000.
If however you'd prefer to design the mod to be cut into maps, with each map depicting a certain part of Blood Island, you could probably do this project a lot more nicely. It'd be slightly less immersive, but you would be able to devote a lot
more detail to each area of the island (no nasty LoD issues to worry about!) and also use engines which were previously unfeasible because you'll be rendering smaller areas at once. Source could be a really nice engine if doing this, since that's what it's designed for. Doom 3 less so, but since it's a night map you'd benefit from its advanced lighting capabilities.
Edit: Another benefit of splitting it into maps is that you could release the mod as beta after getting a couple done, which could in turn provoke people to help you out and work on other maps. The Source community in particular is great for this, with many talented people willing to do work for free if they see a mod has potential (ie: completed work ... trying to recruit really good mappers with no existing material is near impossible). Source probably does have one of the better editing/mod communities around, which would seriously help the mod get both exposed and played.
Edit x2: If this mod gets cancelled after my writing of these long posts, people shall die!