Yeah, a Vandy undergrad degree, despite what lots of people want to believe, isn't much more impressive than an undergrad degree from anywhere else. The undergrad degree nowadays is just a piece of paper one has to have to get in the door, and UT students in particular have just as many, if not more, opportunities to get their foot in the door with the right network.
In my experience, the name of the institution at the top of the diploma is key at only one point of the hiring process: deciding who to interview.
You get 100 applications for a job opening, and have to whittle it down to about 10 or so to invite for an interview. Seeing a name like "Harvard" or "Princeton" or "Duke" or "Vandy" in the c.v./bio piques a little interest and may help get an applicant into the shorter stack. But it's never just that alone, it's ALL the stuff in the application. So minor advantage.
Unless of course, the folks doing the hiring are fellow alums...then there might be some outright preference. But that cuts both ways.
What is he paying for his tuition? What kind of debt is he in coming out of college? I'd say the UT kids are starting out on a better foot right out of the gate.
UT is a big state school. You can do as well or as poorly as you want, and make as much or as little of your time there as you choose. Nobody will hold your hand like they will at an overpriced private school, but there is no reason you cannot be very successful with a UT degree.
Little known fact: Vandy is one of a handful of private institutions who are ROLLING in endowments, and must keep them in balance to meet some federal guidelines. So they underwrite a SIGNIFICANT portion of undergrad student's costs of attendance based on the family's financial standing. Up to 100%.
So depending on the family involved, it might be a LOT less expensive than you're thinking to go to Vandy. Unless you're rich, then they'll charge you full price, of course, hehe.
But I agree with you on this: doesn't matter where you go to school, if you're bright and a hard worker, you've got a leg up on anyone who isn't as hard-charging, no matter what their diploma says. Saw that all the time in the military--some folks think West Pointers have the advantage over ROTC or OCS officers, but they don't. It's the bright one who hustles who is going to get the promotions and key assignments, no matter where s/he came from. Every time.