Answer
$0.10M$ $NaCH_3COO$ is more basic.
Work Step by Step
** You can find the $K_b$ values on table: 14.2 (Page 624)
Since both solutions have the same concentration, we just have to determine which compound is more basic:
-$NaNO_3$:
It is a salt formed by $Na^+$ and $N{O_3}^-$.
$Na^+$ has negligible acidity, so, we don't need to consider it.
$N{O_3}^-$ is a very weak base with $K_b = 5 \times 10^{-16}$
- $NaCH_3COO$:
It is a salt formed by $Na^+$ and $CH_3COO^-$.
$Na^+$ has negligible acidity, so, we don't need to consider it.
$CH_3COO^-$ is a base with $K_b = 5.6 \times 10^{-10}$
$CH_3COO^-$ has a greater $K_b$ value, therefore, it is more basic.
So, $0.10M$ $NaCH_3COO$ is more basic.