Well the first thing to remember is that they do two entirely different things in most cases. Aftershaves are designed to sterilize the skin and deliver fragrance while balms are designed to soothe, moisturize and repair the skin. Balms by definition contain substantially less fragrance than aftershaves which is the way it should be, Aftershave 'toners' are basically in the same class as balms in most cases.
If you have sensitive skin, or skin that reddens after a shave then I always recommend an aftershave balm first (the Stray Whisker After Balm is an excellent fragrance neutral balm for example), to provide a barrier between the skin and the alcohol in the aftershave and to begin skin repair as needed. All of these factors are dependent on the balm being of high quality, and containing a correct number, and quantity of compounds.
In the case of AP Reserve aftershaves however this is not necessary, my aftershaves are designed to replace balms and I have used specific compounds in specific strengths so that you get the best of both worlds while maintaining a high fragrance component. I did this as for many months in Australia the weather is not conducive to applying a balm without it becoming unpleasant or too heavy and I wanted to deliver a high strength of fragrance that goes the distance.