You will need to know the following;
1 - the maximum numbers of hours of full rated output possible from a PV module at your site. (see link below)
2 - the maximum number hours the existing sump pump must run during daylight hours. Assuming you want the pump to run directly from the PV module(s) with no batteries.
3 - the voltage and amperage of the existing sump pump or the voltage and wattage.
I will invent examples of these "need to knows" to give you a calculation to help you decide which is cheaper.
If the existing sump pump runs on 120 vac (volts alternating current) and it draws 2 amps that would be 240 watts.
The maximum number of hours to run and the maximum number of hours of full rated PV output would be basicaly the same without batteries. I will say a yearly average of 4 hours a day. So we are looking at what might as will be 1,000 watthours or another way of saying it... a 300 watt PV array, a 300 watt pure sine wave inverter with a drip proof box to keep it in, and a voltage controller to keep the inverter from shutting off because of to high of voltage from the PV array. The last could be achieved with a deep cycle battery and a simple on/off charge controller and an on/off load controller. Rigging it this way may even extend the pumping just a bit each sunny day. Just a reminder... 300 watts at 12 vdc nominal is 25 amps, at 24 vdc 12.5, and at 48 vdc nominal 6.25, have I confused you at all yet? There is more! You will have to decide which nominal vdc (volts direct current) to use because this will determine the size wires and fuses that will be needed for the system. Does the existing sump pump have a float switch? Does it every "jam up" with debris? Or is it very clean water?
The other way simply involves using a vdc pump and no inverter of course and there are vdc pump controllers on the market but you will still need to know watt hours for the vdc pump. As far as which one is cheaper... you will have to decide that. So here are some places that might help you to decide.
http://www.solarsolutions.ca/Agri/index.htmlhttp://store.solar-electric.com/sodcwapu.html?gclid=CL-Ly4fdkIsCFQE6gQodhlsHRghttp://www.etaengineering.com/waterpumping/intro.shtmland lets not forget our gracious host the Alt E Store I am sure they have something in store for pumping water as well!
Here is a web site to help determine the numbers of Sun hours I wrote of above. Your site may vary.
http://rredc.nrel.gov/solar/old_data/nsrdb/redbook/atlas/I hope something here helps!