Before everyone gets into the tone differences of the two types and balanced and unbalanced signals let me offer a suggestion supported by the satisfaction I have with my setup. Avoid the Leslie amp all together. Note that I am not suggesting that you avoid using a Leslie. Rather, I am suggesting that you use a Leslie that is powered alternatively. I, personally, use a 22H type of Leslie powered by an Orange head. The advantages that I've experienced include: more volume, greater overdrive options and (in response to your concern) EQ control. Ultimately I plan on picking up an Ampeg B25B head due to the tube setup (they use 6550s and 12AU7s, just like the Leslie amps and are much less expensive) but the Orange was available (I'm also a guitar player) and, nonetheless, sounds great.
There are also companies that make EQs that mounton the organ itself, which could also assist you with your concern.