Filtering on time or frequency domain?
Mathematically or information-wise, you're doing the same thing.

However, filtering in time domain means convolving the signal with a filter kernel, so the algorithmic complexity would be something like $O(n^2)$ in terms of float additions with $n$ the length of the signal.

In frequency domain, filtering is an element-wise multiplication which algorithmic complexity is at most $O(n)$. You also have to consider the complexity of switching between time-domain and frequency-domain, meaning using an FFT algorithm. The FFT complexity is most of the time $O(n\log(n))$. 

So the overall complexity of frequency domain filtering would then be $O(n\log(n))$, which is way more efficient than $O(n^2)$.

Considering for example a 1024-long signal, time-domain filtering would need more than 1 millions operations, while frequency-domain filtering would need approximately 3000 !