Player $A$ has a winning strategy. Player $A$ first takes the number $2$. Then whatever number player $B$ takes, player $A$ takes one with the same last digit. He does this until he can't anymore. But before player $B$'s move, there's an even number of every ending digit except for $1$, so this strategy stops once player $B$ takes the last number ending in $1$. After that player $A$ takes any number, then continues the same strategy. This ends once player $B$ takes the last number with the same ending digit as this one. Player $A$ just repeats this strategy until all numbers are gone. Now player $A$ and player $B$ have numbers ending in the same digits, except player $A$ has a $2$ and player $B$ has a $1$. But each has $100$ of each other digit, so $A$'s sum ends in $2$ and $B$'s ends in $1$, so $A$ wins.