If your power brake booster (the large roundish metal thing that the master cylinder is bolted to) either fails or loses its source for vacuum then your brake pedal will become very difficult to push like if you have manual brakes.
The 1967 Ford Mustang had hydraulic brakes
power
It may have either manual or power. I am not sure if the factory put them on but I have seen them with power brakes. To tell if you have MANUAL brakes look for the master cylinder ( this is where you add brake fluid ) and see if it is attached to the firewall directly. if the master cylinder mounts to a some what large round unit with a large black approx. 1/2 " diameter vacuum hose attached to it it is POWER brakes.
I would say a vacumn leak. Check hoses, measure vacumn with running at idle and at idle when brakes applied. This assumes you have power brakes and it idles well without the brakes applied. Please make sure that the clutch is working properly... Does your clutch work properly?
power brakes are more powerful
The power steering pump also provides power for the power brakes.
on some vehicles the brake booster is operated by the power steering system.the booster operates on power steering fluid instead of vacuum like other vehicles.
One possiblity could be the power brake booster is shot. When you apply the brakes it creates a large vacuum leak, enough to stall engine.
show me where to add power sterring fluid to my 1999 beetle
If the clutch is not slipping, I would say the transmission is fine, the engine may be the reason for the lack of power.
Front brakes have significantly more stopping power than rear brakes.
The stock manual brakes are very effective. Some people upgrade them to a power brake system, which is fairly easy to do, but I am very comfortable with the stock brakes on my 1960 Ford Falcon 4-door. It is my daily driver and I put at least 40 miles on it daily.