I left the 121 world two years ago for a part 91 corporate gig flying a Citation. IMO, it was the best career move I could make. YMMV obviously since each corporate job (just like any other sector of aviation) has its own up and downsides.
The biggest thing that would concern me is the fact that the department is an upstart. Owning and operating an aircraft (for personal OR business use) is an expensive endeavor. You really don't gain an appreciation for exactly how much until you start flying in this environment and signing receipts at FBOs ($700 for catering for 5 people, $5000 in fuel, $200 in ramp fees, etc) and seeing maintenance bills ($10000 for unexpected TCAS failure/replacement, $30000 for burnt out EFIS tube, $250,000 engine inspection, etc).
Many owners (particularly first time) don't have any clue either until the bills start coming in. (To give you an idea a small jet operator can easily reach into the hundreds of thousands per year for operating costs- and that's flying only 200-300 hrs in a Citation or Beechjet.)
QOL of can be much better with a corporate gig. If they are willing to do the 8-hr thing than more power to you! I work a set schedule right now... M-F I'm on a long leash from 7am-430pm. During this time I need to be legal to fly, but there is no established call out time. I can do whatever I want around town, but you can rest assured that if I do get called, I'm going to get out there as soon as possible. That said, in two years of working for this company, I've had exactly one call with short notice. Usually we get notified of trips well in advance (days if not weeks or months). Weekends are off unless prescheduled, and last year I flew 5 weekend days total (all major holidays were spent at home guaranteed off).
Job security is always an issue, but also consider other benefits that might be possible beyond salary. My gig is an expense account operation. We don't get paid per diem, but instead the company pays for expenses. As such, there's no "leftover" cash like at the airlines when you eat frugally, but we eat a lot better on the road. (We budget on $75/day average per crewmember, but splurge from time to time as well). We also have an excellent retirement plan (401K match to 125%) and profit sharing as well.
You have a tough decision to make, but I would make it based on what you think that potential is for job security, the type of flying you prefer, and your own personal attitude towards aviation and customer service. Do you have issues with arranging catering or carrying/loading luggage? Are you flexible enough to handle schedule changes or work around problems that might arise (such as weather or delays)? Can you handle doing flight planning and other common corporate aviation related duties (such as basic cleaning in the cabin and some paperwork?) Regardless of whether they say "no additional duties" I'd expect there to be some additional tasks from what you're used to doing at the airlines.
Overall, I love my corporate job. I'm treated well and am well paid for the amount of work I do. I'll never make what a major airline captain makes, but I have a much better QOL than any airline pilot. In the end, it's a trade off that I'm more than happy with.
Good luck with the decision!