If you really want to estimate the accurate value for offering a purchase price, you should not use an online valuation site, free or subscribe to. The two you mentioned and many others get their data only from county records and their algorythims do not filter or separate prominant differences. They provide ALL transactions recorded therefore the values presented vary greatly.
If you do choose to use the comps presented, you need to research every transaction and property details to filter out those that are not valid comps and use the ones that truely are. You would need to pick the ones that are arms length transactions, exclude distressed sales such as short sales, trust deeds, and bank owned sales. You would also need to choose the most recent sales closest to the property, closest in square footage, design, construction, condition, and amenities. If the property is a 2 story home you need to filter out the 1 story homes and visa versa.
Others have mentioned getting an appraisal, which would be good, however, your lender will order an appraisal once a purchase agreement has been signed. You could contact an appraiser before making an offer and request a consulting assignment to help determine a purchase price which would be more in line with the appraisal your lender orders. The other option would be to contact an agent who understands the proper process of choosing comps and not just cherry pick what is needed to make the deal work. You would also need to take into consideration the rehab costs in your offer. If the property is in a declining market, your lender will most likely require an additionl 5% down if being funded through a federally funded financial institution.