The Air Tour Operator's Licensing (ATOL) scheme requires tour operators and travel organisers to participate in a compensation scheme so that customers will get their money back if the company goes bust. The scheme is administered by the Civil Aviation Authority, which will also arrange for any customers, stranded abroad by the collapse of an ATOL company, to get back to the UK.
Flights purchased directly with airlines are never covered by the ATOL scheme, since they're excluded from participating in it. (The only exception is where an airline actually runs its own tour operator's business, selling charter flights on its own aircraft).
So booking your flights directly with an airline always carries a slightly greater (theoretical) risk than buying through an ATOL operator. However while there are a few airlines which are probably struggling to survive, easyJet certainly isn't one of them. Like its big rival, Ryanair, easyJet is one of the world's most financially secure airlines. So you can safely ignore the advice of First Choice, and go for the cheaper option.
http://www.caa.co.uk/default.aspx?catid=1080&p agetype=90
Chris