Comparing growth of two sums of functions
Yes, asymptotically. You can see that $n + n^4 = \omega(n^3 + n^2)$ by taking the limit:

$$
\lim_{n \to \infty} \frac{n^4 +n}{n^3 + n^2} =  \lim_{n \to \infty}\frac{n + n^{-2}}{1 + n^{-1}} = + \infty
$$.

See also this answer.