I've done both (4.5 years in 91/135 and currently 4 years in 121). To sum up this debate in one phrase: With corporate: You live to work. With the airlines: You work to live. It is that simple.
As a corporate pilot you work at the pleasure of a company and/or a person or group of persons. You go where they go, when they want to go and for how long they want to go. The schedule can change on a dime and most of the time there is no schedule at all, just a vague "time frame" as to when a trip will occur. Your time off, especially vacation, is arranged so that is convenient for the company and/or persons you are working for. Even when you are "off" you are still considered "on call," so yes, while you are at home, you still cannot plan anything as the phone might ring at any moment. The training is suspect unless they send you to FlightSafety or SimCom on an annual basis and the "standardization" amongst crew members is a joke. Promotions are a slippery slope as it is always cheaper to hire an outside pilot with a type rating in the airplane before spending the money on you to get your type. Lastly, when the company's balance sheet starts to head south, you and your airplane are among the first to be let go, and in many cases without warning. That is simply the nature of corporate flying.
Now, some people will get on here and claim that as corporate pilots they are making huge sums of money with a set schedule and training regiment...while there are some pilots fortunate enough to have this situation, the overwhelming majority of corporate pilots have zero schedule, making barely decent to OK money and have very little control over their life.
In the airline world, you work to live. If you want to make a decent amount of money, you can, if you want to work as little as possible and still have a 75 hour guarantee each month, you can. While your quality of life and schedule are always dictated by your seniority, as you spend more and more time at a carrier, your seniority will improve, the hourly rate you have will go up, the schedule you can hold will get better and as long as the carrier you're with doesn't go out of business or shrink to half its size, you will upgrade to Captain. The training associated with the airlines is second to none, the standardization and actual flying processes are beyond outstanding and the overall nature of the job (in my opinion) is performed at a much higher level than at most corporate flight departments. You have travel benefits, set vacation weeks that you can bid on, the ability to arrange your schedule to your liking (relatively speaking) and many other tools that can allow you to tailor your schedule to maximize your quality of life.
Of course, not everything is roses in the airlines either. You have the whipsaw game, potential of furlough, incredibly low first year pay, unpredictable upgrade times and many other factors outside of your control that can affect your quality of life in a negative way. At the end of the day though, I feel that the airlines represent a better job overall to a pilot when you consider quality of life, schedule, pay, training, job security and career potential.
That is my $.02 on the matter. At the end of the day, do exactly what you want to do and do what is best for yourself and family while considering your future in the aviation field.