Auctionator has a more minimalist UI. It provides real-time searching, a "memory" for any scanned auction data and prices, and a more powerful search and posting UI than the stock.
Originally Posted by Icecreamtruk
TSM took all of that a step further by integrating it to professions and crafting, as well as providing a graphical interface to set up features like auction "rules" to govern all the when and how things about auctions. It also provides some more powerful scanning options and the ability to remember all scan data externally (and update it from external sources!), the ability to see most recent cost and profit analysis, and a whole slew of features I don't even use and can't accurately describe.
Many people, myself included, feel that Auctionator is really what Blizzard should have coded the AH UI to look and function like. It basically takes the stock UI and extends it to be more friendly to power users.