Welcome to Stangnet.
This is definately a subject everyone will argue over. Some people will prefer a stock classic, others a high performance muscle machine. It's your car and your the only one who will be able to decide.
Before you start tearing into it, you may want to see if you have the original engine in your car. The car might be worth a lot to someone else if it's all matched up.
Whatever your choice is, people here will be more than glad to help you out.
Good luck.
The one on the left...65 coupe, manual everything, TCP R&P, TCP uppers, front and rear sway bars, stock ride height, 15x7 TTds with 215 60 15 tires, 180 rwhp (dyno tested) from the 289 with a close ratio toploader, 3.25 trak lok rear, two tone pony interior, front disc manual....blast to drive
The one on the right 65 fb, restomodded out the arse....manual everything, 408 stroker cleveland, lower 1.5 or so inches, stock style uppers, roller perches, front and rear sway bars, late model seats, 17x8 TTiis, 4.11 trak lok, overdrive auto transmission with 4r70w gearset, going to the dyno in a week should be 400 rwhp, 4 wheel disc brake...blast to drive.
The one on the left has so far been alot more reliable and cost a heck of a lot less to build
The trick is to decide
First: your use
Second: your mods to achieve use
Third: you budget
If the budget you lay out is not enough to achieve the second, you need to rethink the direction, the parts, or the use. The left car is a fun dependable daily drive stang that can still hang with alot of cars out there, can go to the road course if need be or the drag and be alot of fun. The car on the right is a weekend warrior car that had major scope creep on the resto project of building a car to take to the 1/4 and road courses for fun but capable of driving to both under its own power.
id say depends on the options it has. if its a drum brake, no power steering, 2v, no ac, ugly color combination car, Id build it fast. Cuz those no option cars are all over the place. Now, if you had a 4v 65 GT with AC, ps and front disk brakes all with the original tranny, motor, then Id say keep it original....
my suggestion is build as YOU like it. if you dont you will end up not liking the car as a whole. i would suggest though that you dont make any mods to the car that cannot be reversed unless you plan on being buried in the car. otherwise you may find it hard to sell shold you ever reach that point, and if you go too far with mods, you may end up not driving it because you are too scared that your expensive body work will be damaged by some idiot in a parking lot.