My brother got a new '65 Mustang and I got a new '67 Mustang. Both had 289 V8’s and 3 spd manual transmissions. Compared to current cars they are very unsafe.
My '67 had drum brakes all around and did not have power brakes. Braking was fine in dry conditions but did take a lot of foot pressure. Since no new drivers since the 70’s have never experienced non-power brakes you will find the pressure needed to stop the car to be excessive. And stopping distances very long.
When the drum brakes got wet, as in after going through a puddle on the road then you have virtually no brakes until they dried out. Drying out the brakes is also something no new driver has ever done. In effect, you apply brake pressure with the left foot while maintaining speed with the right foot on the gas until you feel the brakes starting to work again. It can take 2/10ths of a mile or so for the brakes start to work again - not safe.
The unibody was pretty skimpy by current standards so a vintage Mustang hit from the side will not do much to protect the driver or other occupants. The gas tank is just under the trunk and does not do well in rear end collisions. It wasn’t as bad as the Pinto, but not that much better either.
The front and rear bumpers are completely useless. They give no protection at all. A very slow speed bump will dent sheet metal and prove to be an expensive repair. Parking lot impacts that do no visible damage to a modern car would do a bunch of damage to a vintage Mustang. I’d park it far from other vehicles if you go to the grocery store or local mall.
Now handling, good for the era but like an untamed beast by modern standards. My '67 came with Wide Oval Firestone tires. They were awful, hydroplaned at 30 mph, and were worn out in less than 12K miles. I found some Dunlop radials in the wide oval size and they were much better. Even with the Dunlops the back end of the car would hop wickedly to the side when taking a hard turn on uneven pavement. In a modern car the reviewer would call it unacceptable. Back in the day most lighter weight rear wheel cars with V8 power did the same thing, but the Mustang was really bad in this regard. How your vintage Mustang handles will depend on the tires you run on it, very good shocks, pretty hefty springs, and still it will just plain hop around on rough pavement no matter what you do.
The cars were and still would be fun to drive, but they are simply unsafe compared to even the poorest scoring current model cars. I haven’t driven a new version Mustang, but I’d bet that a V6 Mustang with a manual transmission would be a hoot to drive and not far off the performance of my '67. A V8 would out perform my '67 on all fronts. If you are looking for a daily driver, test drive a NEW Camaro, Mustang, or Charger and you’ll save money and have fun.
If you just want a vintage Mustang as a hobby car, to take to shows and for nice weekend drives go for a well restored one. Just make sure it has a V8 and manual transmission if possible. The original 6 in a vintage Mustang is just a dog and not fun to drive at all, looks great but no guts. The auto transmission a vintage Mustang is the same auto tranny used on most Fords of the day. It was a 3 speed unit with a floor shift set up. D, 2, and L gave you some opportunity to select the gear but it was a pretty sloppy shift and just not nearly as fun and connected feeling as a 3 or 4 speed manual. The power loss was notable in the auto tranny since the torque converter was very inefficient by modern standards.