Both sites serve a similar purpose - to let you see reviews and make contact with tradespeople in your area. The main differences are that Checkatrader has a bigger reach and advertises often, but they don't limit the number of traders in any area which can overwhelm you with responses.
In contrast, TrustATrader doesn't have as big a marketing reach, but they do restrict the number of people within a certain trade who can be members. The aim is to make sure only high quality traders work on the site.