Most people that recommend TAOCP haven't read it; and IMHO it's highly overrated.
I've read parts of volumes 1 and 3. This book is awesome if you have the time to digest it, but you get faster results from other books that are easier to read, like Cormen's Algorithms.
It depends on the results you want to get-- TAOCP and CLRS are completely different creatures.
If you are expecting TAOCP to be an Algorithms textbook, you're going to be severely disappointed.
Personally, I find TAOCP to be highly underrated. I find Knuth to be an utter joy (and just yesterday, greatly enjoyed watching the video of the 16th Annual Christmas Tree lecture.)
CLRS is a great Algorithm textbook, but it's not the place to go to find why there is a Pi in the formula for the approximation of Catalan numbers.
I liken TAOCP to Proust. Fawned over by a small subset of people (rightfully so), a larger subset who talks about it but doesn't actually read it, and shunned by the majority as dense and intimidating.
I'd agree with you on Cormen's Algorithms but the original post already mentioned Algorithms (which could mean one of two texts that are considered standard in the field but both cover about the same territory).
But I'd be interested in knowing what books you refer to as far as giving faster results beyond that(TAOCP is dense which I'll agree makes it a difficult read). I've never found a book that covers the same information as TAOCP and while I hated every second of reading it when I was being forced to do so I have to admit the knowledge has served me well
I've read parts of volumes 1 and 3. This book is awesome if you have the time to digest it, but you get faster results from other books that are easier to read, like Cormen's Algorithms.