This question arose on a comment thread over on ELL. Are there any rules or patterns for when we should/do select "ish" as a suffix, rather than "like"? Some examples discussed were that birdlike comes naturally and is easily understood to mean like or in a manner such as that of a bird, but no native speaker would come up with birdish. As for the opposite, there are words such as cliquish, which clique-like would never be substituted for.
Another interesting point that FumbleFingers raised in that discussion is that we have some words which take the suffix ish but clearly and recognizably do not mean "x-like", such as "sheepish". (Perhaps the origin of sheepish is something along the lines of that sheep (the animal) act sheepish, but when you say "He looked away sheepishly" you don't mean "he looked away in a manner similar to that of a sheep.")