I am not familiar to the policies of Ohio State or Purdue; but generally, they have their own Standard Operating Procedures ("SOPs") and will require you to fly to their standards. You will likely receive at least *some* "credit for having a PPL and instrument rating;" but you will probably have to take an equivalency checkride with a university check pilot... irregardless of whether the PPL and instrument training was done under Part 141. As to whether they employ you as a CFI, that would depend on if they are hiring; if they are hiring, I would see no reason to why they wouldn't hire you (assuming that you've completed their program to satisfactory standards).
Being a graduate of one of the largest aviation universities in the nation, I'd suggest that you attend an in-state public university. Out-of-state tuition at a public university is often equal to or more than the tuition of private universities; you'd be better off going to a private university if you are considering an out-of-state public university (specifically, due to better value and smaller class sizes). In-state university tuition at a public university is a bargain -- and you'd save yourself a ton of money and potential loans (depending on your financial situation). Even better... consider community college for two years; then after you graduate, transfer to an in-state public university.
Nonetheless, if you're set on attending a big aviation university, be forewarned that such universities rarely afford an advantage over students trained at small flight schools. Perhaps you will be afforded preference for internships at major and/or regional carriers and the opportunity to network with future aviation professionals; however, the advantages generally end there. Moreover, by attending a Part 141 -- or Part 142 -- university program, you will be spending more time in the classroom and less time flying (the little flight time that you accrue will be charged at a premium). There is no difference between a flight certificate earned at a Part 61, Part 141, or Part 142 program; nor do airlines care to where you earned flight certificates. I highly suggest a backup degree in a subject other than aviation. Nonetheless, you asked for the "pros and cons" -- and I will provide you with my following opinion:
AVIATION UNIVERSITY:
Pros:
- Opportunities for internships which may lead to reduced hiring minimums (depending on current economic conditions).
- Opportunities to network with future aviation professionals; such networking may lead to future job opportunities.
- More of a structured environment -- as in addition to your ground school classes, you will likely be taking classes to further enhance your knowledge to aviation (ex. Aerodynamics, Aircraft Performance, Aviation Law, Engines and Turbines, Meteorology, Systems, etc.).
- You will breathe, eat, and live aviation; ask yourself, is that something you really want? If so, then go for it... but weigh the pros and cons carefully.
Cons:
- Generally, flight and instructor rates are much greater; you will pay more.
- Less scheduling flexibility.
- More time in Flight Training Devices (FTDs), Flight Simulators, and cockpit mockups.
- No difference in the FAA certificates that you receive.
"UNAFFILIATED" FLIGHT SCHOOL:
Pros:
- Complete flight training at your own pace; then afterward, flight instruct to accumulate flight time. Flight time is one of the most important factors in getting hired (*much* more than where you attended college - or - where you completed your flight training). You can work as a flight instructor at a small flight school while completing your college degree. Then once you graduate, you will have valuable CFI/PIC time that will likely qualify you for the regional airlines.
- Generally, cheaper flight and ground instructor rates.
- If you train under Part 61 or 141, you will certainly get more actual flight time when compared to training under a Part 142 program (some aviation universities operate under Part 142 requirements).
- No difference in the FAA certificates that you receive.
Cons:
- Generally less sophisticated aircraft.
- Less of a structured environment.
- Less opportunities for aviation-related internships and arguably, networking.
- You won't get to totally immerse yourself in aviation (if that's what you really want).
In summation, I cannot stress the importance of becoming a flight instructor to build hours (PIC)... there is rarely a way around it (except for perhaps the military route); multi-engine PIC time is particularly important to getting hired by a regional airline (ex. Seminole, Seneca, etc.). Moreover, try not to fail -- or "bust" -- any checkrides; they have become increasingly scrutinized since the crash of Colgan Flight 3407. Some airlines have even established a limit of no more than two busted checkrides to get hired as a first officer.
Whatever option you select, fly safe, fly smart, and study hard!