Autenrieth is more of a beginner’s dictionnary. The definitions are very short. It’s an old book, from the XIXth century, and actually it’s a translation of German original work. There are nice illustrations, “plates”, that help you understand what those ship part names and other technical Homeric terms mean.
Autenrieth is in the public domain, so you can get it free on Perseus. Also an iPhone app called Lexiphanes includes Autenrieth. But you have to buy the book, if you want to get the illustrations too.
Cunliffe is for more serious readers. For every meaning of every word (or almost), it gives a list of all the places where it occurs in Homer. The definitions are longer, also. As it is more exhaustive, it takes of course a bit longer to find what you’re looking for than with Autenrieth.
So: Cunliffe is better, Autenrieth is quicker and has a few nice illustrations. I have both.
Cunliffe is way more comprehensive and cites specific lines from Homer where each word can be found, so it’s almost like a concordance. too. If my copy of it–the U. of Oklahoma edition currently available on Amazon–hadn’t fallen apart at the spine after a few uses, I’d recommend it wholeheartedly. If you don’t mind the pages falling out every time you use it, get Cunliffe.