Is there any way to differentiate between impulses?
If you are looking at vectors $\mathbf x$ and $\mathbf y$
(presumably of the same length) in which the entries are
mostly $0$s and


with occasional $1$s (unit impulses), a good measure of the difference
between the vectors is the Hamming distance between them, that is, the
number of samples in which $\mathbf x$ and $\mathbf y$ differ
with occasional non-zero entries (impulses of different amplitudes),
then we need to distinguish between impulses of different amplitudes
but the same location. If we use Hamming distance, then the measure
of the difference between
$$\cdots \quad 0\quad 0 \quad 0 \quad 1 \quad 0 \quad 0\quad 0\quad \cdots$$
$$\cdots \quad 0\quad 0 \quad 0 \quad 2 \quad 0 \quad 0\quad 0\quad \cdots$$
and
$$\cdots \quad 0\quad 0 \quad 0 \quad 1 \quad 0 \quad 0\quad 0\quad \cdots$$
$$\cdots \quad 0\quad 0 \quad 0 \quad 9 \quad 0 \quad 0\quad 0\quad \cdots$$
is the same which is not quite capturing our intuition that the two pairs
are more different than the Hamming distance is telling us. Possibilities 
to consider in this case are
$$\sum_{i=1}^n |x_i - y_i|,\quad   \sum_{i=1}^n |x_i - y_i|^2,\quad 
\mathrm{or}\quad \sqrt{\sum_{i=1}^n |x_i - y_i|^2}.$$
The last quantity is the Euclidean distance between the vectors. Which
measure you want to use depends on how much the measure captures the
features relevant to your application.