The number of players question is key - War of the Ring is really a 2-player game. MEQ can support 4...
However, I personally prefer War of the Ring. I feel the game is more evocatve of the Lord of the Rings and Middle Earth theme than Middle Earth Quest (which is still a good game by the way!). War of the Ring contains all the elements that are best associated with the Lord of the Rings, and the general design and look of the game is wonderful.
Middle Earth Quest also hits the theme, but it is a harder mark for the game due to it not containing as immediately recognisable aspects such as the fellowship and so forth. The spread of influence is really neat, and the opportunity to 'meet' and interact with elements of the Lord of the Rings story before the story happened is handled in an interesting way. War of the Ring just manages slightly better in my view.
The graphic design of Middle Earth Quest is recognisably FFGs fantasy style - the lettering, borders, illustrations and so forth wouldn't look out of place on any of their fantasy games. For me it misses ever so slightly the mark that War of the Ring manages to hit - with better selections in these things making a visual package that better evokes the theme - though this element is also highly subjective and may or may not take a role in your experience of the games.
All in all, I like War of the Ring a lot. I like Middle Earth Quest, and am looking forward to playing it more, but if there had to be a winner, I'd give it to War of the Ring by a narrow margin.
Again though - I don't think you'll be losing out with either game, and really the choice would probably be best made for whichever game you'd get to the table more often!