^^ Those are technical specs and only give a glimpse of what the headphones will theoretically able to do. How they sound in practicality differs based on the the overall acoustic engineering and which boils down to every last bit of detail in the design including the ear pads. For instance every headphone out there differing in price from Rs 200 to 50,000 or more may advertise a frequency range of 5Hz~22KHz. Even if everything else in the specs is the same, they still won't sound the same.
The exact same driver may behave differently based on the ear cup design, ear pads, the kind of connecting cable used, the source etc.
As an example, take a look at MrSpeakers Mad dog headphones
https://mrspeakers.com/mrspeakers-mad-dog-headphones/
What they do is use a off the shelf headphones called Fostex T50RP which don't cost a lot and then mod it and the end result is the Mad dog headphones which cost a pretty buck and apparently justify every bit of that cost.
What you buy depends on how you like your sound. Audiophiles have their own tastes based on the kind of music they like. Professionals typically prefer flat/neutral headphones. Gamer's look for positional audio.
Regarding the AMP, you will need it for headphones with high impedance rating. For the typical 32 ohm roundabouts, you don't need a dedicated AMP. However some headphones in that range apparently do sound better when driven through an amplifier even if they don't need the amp for the getting the desired amplitude.