I have worked as an EE for an electrical contractor, an AE firm, a hospital, a MAC conference university and on my own. I have also done "moonlight" work while being employed by all of the above except myself so maybe I can help.
If you are working for an AE you may work on multi-million dollar electrical projects such as new schools, high-rise office buildings, treatment plants, power plants, factories, university academic and athletic facilities, campus medium voltage distribution etc. You may or may not be solely responsible for electrical design and drafting but more than likely on bigger stuff you will have other engineers and draftsmen on the same project. You may only do the lighting, or power, distribution, or alarms or communications or some combo. Of course, you probably work on smaller stuff too but usually larger projects than Joe Moonlighter, PE can handle himself.
Working on your own as a moonlighter you will likely be working on small apartment buildings, dentist offices, light commercial offices, parking lot lighting, small building additions etc or maybe a specialized project such as to solve power quality issues. You will also likely have to do all the design and drafting yourself. Oftentimes clients are developers or electrical contractors who don't like to pay promptly and will be looking for you to be cheap and fast. That is why they are looking to you and not an AE firm for help. Not because you are so much better, but because you have a stamp and will likely be cheaper and faster than an AE firm with overhead costs.
Lazlo is correct too, arc-flash, short circuit, coordination studies are also opportunities but just getting started you are looking at what I mention above.
I highly recommend getting professional liability insurance if you decide to do this. I use a company called PDI out of Indianapolis but I am sure there are others. I also recommend charging fair market rates to A) Make it worth your time and B) because taking jobs too cheap hurts the whole industry.
I think it is ridiculous that AE's will take projects for 7% - or less - sometimes with reimbursables and sometimes not for all the work and liability that goes into a project - but a realtor also gets 7% - for doing what?????
(Note: contracts and projects are different. I don't mean to imply 7% is standard. I have seen fees lower than this and much higher than this. Just using it as an example.)