I have LSJ, Middle Liddell, Little Liddell (I don't need all three, but each time I thought I needed an upgrade...
), Cunliffe and Autenrieth.
If you have Cunliffe, you don't need LSJ, Middle Liddell or Little Liddell to read Homer. I agree with jswilkmd that if you need one dictionnary to read just Homer, get Cunliffe.
The reason I like Autenrieth is that it's really quick to use. The entries are really short and you find what you looking for quickly, especially with commoner words that tend to have really long entries in other dictionnaries. You don't get any details or any nuances, so I woulnd't recommend it as a your only dictionnary, not even just for reading Homer.
Autenrieth and Cunliffe include basically all and nothing but the vocabulary of the Odyssey and the Iliad, so it's of little use for anything else, expect perhaps a little for Hesiod and other (early) epic.