The conditional operator ... Con ... is the tool to use, if you are looking for a particular change combination
Con—Help | ArcGIS for Desktop
I like ... Combine ... Combine—Help | ArcGIS for Desktop
because it 'combines' all combinations of two input classes and produces a table and a raster showing where things were the same, where the differences occured and what those differences were. Reading the table is the key to understanding so take some time to understand the visuals in the help topic. Once that table and resultant raster are analysed, you can use the Con tool to produce rasters of different types.
I should point out that simple useage in the Raster Calculator can check for equality and other operators.
Raster Calculator—Help | ArcGIS for Desktop
There will rarely be one tool that does everything you need, and sometimes it is easier to breakdown an analysis into steps so that you are clear on the outputs as you go along... in that vein, there are basic 'math' style tools with the math toolset of the spatial analyst tools