I'm a little at a loss to what you mean by "like a cake," do you mean "chewy?" Or, do you mean "light and airy?"
Chef peon made some excellent points.
As chefpeon wrote: Always a help, especially with baking. Most especially when the description of the problem is ambiguous.
Yes to this as well.
Sugar has the effect of making cookies crisp, compared to either honey or agave. More likely than not, this is at least partly why you get "like a cake" cookies -- if by "like a cake" you mean chewy.
Another possibility is that you're baking at too low a temperature, and yet another is that you're not cooking all the way through. In fact, the first suggestion I'd make (other than changing the ingredients) is to cook a little longer at a slightly higher temperature.
Most bakers expect a substitution of whole wheat for white flour to result in a much heavier cookie (or any other baked good, for that matter); and heavier is not consistent with "like a cake," at least not in the way most of us think of cake. That may account for some of the confusion. On the other hand, if by "like a cake" you mean "light and fluffy," we all want to know your secret.
If you could be more specific about your recipe -- in terms of ingredients, techniques, times and temperatures -- and perhaps try another description of what you're going for and what you're getting which doesn't include a comparison to cake, it could help us help you.
Finally, as a general rule, oatmeal cookies are supposed to be and are generally expected to be chewy and not crisp -- this has everything to do with the nature of oatmeal and the type of sweeteners (molasses, brown sugar) usually employed.
Keep on experimenting and stay in touch,