If you have to find something there are lots of websites related to in the web quickly, Google is the best searching engine.
But if you find hardly anything related to the topic, use Alltheweb.
It finds really everything in the web related to the string you entered, but there are many hits which arenīt related to the topic at all.
It really matters which search engines and directories the resource that you are looking for has registered with... so saying that one is better than the other for results in some respects is silly (unless the resource is common and has good saturation). There are semantical differences in each that does make a difference in how each provide results, etc, but if what you are looking for isn't registered with the search engine that you are searching on... you will not find it.
Fortunately resources like google and others are so large and powerful that the likelyhood of you finding what you are searching for is quite good.
To tell you the truth tho... there are resources that are more important to the web promoter than search engines... dmoz is probably the most important directory on the web because it services many different search engines (msn, aol, and many many more).
Google powers yahoo search, but being in the yahoo directory brings you a considerable amount of more traffic than the yahoo search.