although I said LotR was the greatest film score ever recorded, that doesn't mean I would say Howard Shore is the greatest film composer ever (though I'd probably place him in the top 10 based on LotR alone). Cases could be made for John Williams or some of the golden age composers being "greater" composers based on their overall bodies of work (personally I'd go with John Barry, but this is entirely biased and based on my own tastes). Williams is/was pretty consistently great, yet none of his scores quite reach the heights of LotR, nor am I certain he could've done something on that level, or whether he'd have just phoned it in like a lot of his other later work. Shore just happened to record one score that exceeded all others. Apparently Horner was considered for the job, but I can't see him devoting as much time and originality as Shore. I'm sure any of those composers would've done good work, but I'm not sure they'd have accomplished what Shore did. If John Williams is Peyton Manning, then Howard Shore is Drew Brees--Manning likely being considered overall a more gifted quarterback, yet Brees was talented enough to aid his team in pulling off one of the greatest upset victories in NFL history. That's about the extent of my sports knowledge/metaphors, so don't read too much into the comparison.
I realize that this is all very subjective, but I think there's good reason to list LotR as the greatest score (I list them all as one because all 3 were written and recorded as a cohesive unit, similar to the way the movies were filmed back-to-back). The amount of time and energy he devoted to LotR is more than most composers give. Typically they spend about 6 weeks on a score. Shore spent 4 years of his life on LotR, reading Tolkien, writing unique themes and motifs for a number of fictional cultures and characters, coordinating more closely with the director than is standard for score composers. Just cannot see many of the other greats giving that much of themselves. Look at Williams' work around the late 90s and early 2000s--he was pretty busy, and I don't see him passing up the SW prequels or Spielberg to do LotR. Even if he had worked LotR into his busy schedule, could he have even made the time to do the research and intensive coordination with Peter Jackson? At best, we might have gotten something on par with one of his Star Wars or Harry Potter scores (yes, very good work, but doesn't quite reach the pinnacle LotR reached)
