Airline managements hold a great deal of power over the pilots. The degree of that control depends greatly on whether there is a union contact in force, or not.
A non-union company has "at will" control, meaning they can fire anybody for any reason, anytime. A union company has strict contractural legally enforceable rules to follow. Non-union company management often times changes company "policy" capreciously (and often) to suit their own purposes. From personal experience, I've been pushed to violate FAA rest rules in a non-union company. Frequently new startup airlines have good labor relations for the first few years. Employees put in 120% to get the biz going and profitable. Managements then milk this good will until the employees see that the company is making large $, and they are being paid grossly sub-par wages. Jet Blue is a new startup and enjoys cordial labor relations, and SEEMS to be trying to break the pattern set in the past. Time will tell if JB management turns predatory like virtually all others have.
Union companies on the other had have legally enforceable contracts. Both the pilots AND management have clearly defined responsibilities and obligations. The rules are clear. Recently however, most major airlines have invoked the rarely/never used clause of "force majuere," and provision that gives management a much wider latitude in times of GRAVE emergency. Most major airlines have some degrees of "no furlough" clauses -- UAL, DAL, and AA. AA's management signed a no-furlough agreement last spring in return for the American pilots' waiver to allow AA to use the AA code on TWA flights. AA now has abrigated THEIR side of that agreement under "force majuere" and has furloughed almost 600 AA pilots, but still uses the AA code on TWA flights.
Bottom line. You are virtually ALWAYS better off with a labor contract rather than without one.