what will be the difference if we do analysis of a system by using time-domain analysis or frequency-response analysis on other end??

Differences are clear and obvious...mathematical tools are different but the results shall be the same. Just do it to validate the answer.

regards

Frequency response methods are suited for linear systems. When considering non-linearities, frequency response might not be applicable.

When looking at the non-linear response of the system, the only available technique is time-domain numerical integration.

If you are doing Vibration analysis, then;

1) Time - to know the exact cause of the vibration

2) Frequency - to know the severity

wallahu a'lam

Frequency domain analysis is very helpful for example in electronic to study the response of the whole system during change of independent output/input parameters (example input/output voltage-current and so on).
Analysis in time domain would be much more difficult because the Mathematical tools are quite different as said by Enrique.
The results are the same but in frequency domain they are more easy understandable