Ziggy's comments seem very to the point to me. I'm not in the business, so take what I say with a grain of salt as I add a couple general observations.
It is likely that if you have a degree/certificate from a more prestigious school it will carry more weight if you are applying for work outside LV. It is likely that within the LV community itself, personal contacts and the weight of your particular recommendations with the particular chef who is considering hiring you will be more important than which school awarded the degree. And your personal accomplishments.
Furthermore, if you take your degree from a cc, it is easier for you to continue on to get a BA/BS by continuing your education at the university. It is not clear that this would be as easily accomplished if you go to culinary school (check with the university to find out). This might make a difference if you change your mind about cooking.
Mostly your answer is within yourself: what are your personal ambitions as a chef, what is the level you intend to work at. Where on the continuum between the local diner and The Laundry do you envision yourself?
If you see yourself at the cooking as an art end of the spectrum in prestigious kitchens, then the financial investment and sacrifice of a prestige culinary education might be worth it in the the contacts you make as well as the prestige of the degree and the contacts you make while acquiring your degree. If you see yourself at the cooking as a craft end of the spectrum, then it might not be worth the sacrifices. Only you can make these decisions. Either goal is honorable.
Implicit in your questions are broad issues of class, prestige, the cost of buying greater opportunity that most Americans don't want to acknowledge exist. Someone with tons of money and an extensive support network could apply to a prestige school (a culinary Harvard), pack up his/her family and go there. Period. Or they could go to college for 4 years, then go on to either a prestige culinary school or start out, perhaps for free, working in prestigious kitchen (here or abroad), hopping from one to another to build a reputation. People with less money have more constraints, have harder choices.
If you are confident in your ability to learn your craft and exercise it with imagination, if you are good at making friends and impressing everyone else with your character and personality, if you are a focused, inner directed, hard worker, if you are realistic about your self assessments and what your work requires of you, then you will succeed at what you do whichever choice you make.
If as I understand it, your choices do not include the small handful of prestige schools that more or less guarantee you entry into prestige kitchens all over the world. And if, as I understand it, you are probably staying in the LV area, then you might find out where the people who work in the kitchens you'd like to work in (both for a first job and career peak jobs) came from. To my mind that might help you make your decision more confidently whether staying in LV or not. The web is full of chef's bios. Pick the ones you emulate and check out their bios, get a sense of what has worked for others whom you admire.
There are several books by chefs and about becoming a chef. I haven't read Dorneburg & Page's "Becoming a Chef," but I rate their "Culinary Artistry" book VERY high in usefulness; it is very businesslike and use-oriented. I have the impression their other book is also. Perhaps others can suggest things you can reference beyond Bourdin's self-promoting ego trip.
" ...but in the spirit of 'stop, think, there must be a harder way, 'I figured starting from scratch might be more gratifying.'' (Judy Rodgers)