Definitely not. Used wins hands down - just don't go too *old* in the used (and/or stare at the undercarriage and see -- you can clearly see the rust in many cases).
Consider a corolla:
2016 Corolla L-Manual, new, $17,300.
Let's say it lasts 11 years, like your current one. That's 17,300 / 11 ~= $1572/year.
I just found a 2014, used, 40981 miles, for $11,398 (and that's from a dealer)
If you believe that rust, and not mileage, is going to be the most likely thing that kills this car, then the used one should last 9 years. That's 11,398 / 9 = $1266 / year in amortized capital costs. (If it's mileage, it's still only a half a year off -- your 175k in 11 years is 15.9k per year, or about 32k in those first two years, so this car has only 9k more than you would have put on it.)
In general, a car loses a decent chunk of value in its first month and first year, and then things are pretty linear thereafter. Don't be the person who pays for that "drive it off the lot" depreciation. Let someone else do it for you.
(see, e.g., the graph in
http://retireby40.org/dont-pay-depreciation/ )