The state-of-the-art of automotive technology has advanced quite a bit since the heyday of the first Mustangs, or even the Fox-chassis revival of the 1980s.
Compared to that higher standard, the Mustang is a relatively crude car. For example, the Mustang still uses a solid rear axle when most performance cars use an independent suspension.
Ford had its reasons for the axle decision (cost, popularity of axle swaps for drag racing, etc.), but it means that the Mustang's ride and handling are compromised.
Also, while the Mustang is not very expensive, there are many more performance cars competing in its price range (Subaru WRX, Mitsubishi EVO, Mazdaspeed 3, etc.) than in the past. The sophistication of these cars highlights the relative crudeness of the Mustang.
The Mustang is not a bad car, it just isn't a great car.