The Bundesliga champions offloaded Kroos to Real Madrid earlier this summer, before bringing in Alonso from the Santiago Bernabeu side last week.
Schuster feels it's impossible to say who of the two is the better player, but he has stressed that Alonso is the man Bayern needed most at the moment.
"You can't say whether Alonso is better than Kroos. Toni is a more attack-minded player. They could have played together quite well," Schuster told Bams.
"You always have to look at what a club actually needs. And Bayern needed Alonso more than they needed Kroos.
"We will see come the end of the season which team benefited from this transfer the most."
Schuster then went on to compare Alonso to Bayern coach Pep Guardiola during his active career.
"Pep Guardiola brought in his twin with Xabi Alonso. Pep used to play in the same position and had the same playing style.
"Both are strategists in front of their defence and aim to retain possession. They are organisers on the pitch and have a certain responsibility. They are a coach's right-hand man on the pitch."