I've played both Age of Mythology and Empire Earth, so I can do a bit of a comparison. While the core gameplay of both games is the same (resource gathering, base and army building, razing the enemy to the ground), there are some differences between them.
-EE has many nations which share the same generic unit roster, but are vastly different in terms of boons (which can affect anything, from resource gather rate, to research/building cost, to the various statistics of units...), as opposed to the three (four) radically different nations of AoM. Also, in EE you can create your own civilization.
-Resource gathering is much slower in EE, which leads to a much slower first stage.
-While in AoM you get a new God Power and various, deity-dependent upgrades every time you advance an age, in EE you always get some generic enhancements, and no new powers (however, you can use calamities to harass or destroy your enemy; they can be used an infinite number of times, but cost a large amount of "mana" to the Prophet that casts them).
-In AoM, there are those cool mythical units that you must counter with the appropriate units of your nation. There is nothing like this in EE. There are heroes in both games, though.
-EE has a much more epic scope: there are 14 (or 15 with the expansion) epochs, and they embrace the whole human history, from the stone age to the distant future. It means that while there are mostly only minor differences between one age and the next, there are vast differences between one range of ages and the others (for example, first you use stone throwers, then archers, then musketeers, then riflemen, then laser squads). Of course, you can select to play in a certain range if you don't want to go through all 14-15.
So, if you like the base gameplay of AoM and want more of it, definitely buy it. If you liked the unique aspects of said game, you may find EE lacking.