Speakers Power and Quality Difference Factor
A loudspeaker is a transducer which converts analogue electrical signals into sound. To do this faithfully over the range of human hearing, 20 Hz to 20 kHz - a 1:1000 frequency range - is a technical challenge.



Figure 1. Cutaway view of a dynamic loudspeaker for the bass register. (1) Magnet.
(2) Voicecoil.
(3)    Suspension.
(4)    Diaphragm. Image source: Wikipedia's Loudspeaker.

Factors which affect the sound include:


The cone material, its stiffness an surface.
The suspension and how much this constrains the cone movement.
The magnet and coil and whether the coil remains fully in the slot of the magnet during excursion.
The mechanical resonance.
The cabinet or lack of.
The speaker diameter. Large is good for bass but may be poor for treble.


Any non-linearity in the performance of the speaker will result in audible distortion or "infidelity" to the original signal. (High-fidelity, hi-fi, means that the reproduced sound remains faithful to the original.)

In short, the difference you are hearing will be due to the specifications of the device, the design, materials used and care in manufacture.



From the comments:


  Okay , so it's a basically like this : difference between output frequency and input frequency determine quality of speaker.


No. A loudspeaker will not change the frequency. It will follow the incoming driving frequency. What will happen is that if there is distortion then harmonic frequencies will be added to the audio. So, if reproducing a 1 kHz tone you might get slight traces of 2, 3, 4 kHz, etc added to the audio. Guitarists do this deliberately to generate a richer tone by over-driving the loudspeakers.


  I'm assuming speaker's deviation varieties input frequency.


If you mean deviation from flat frequency response, then yes.


  Some speakers better with low frequency others better with high frequency.Also with this logic can I say , generally large speakers good for low frequency and small speakers good for high frequency?


Yes. Large for bass ("whoofer") and small for treble ("tweeter"). The smaller speaker has less mass and therefore can be made to move more easily.