There are two separate questions:
1) Can model of computation X recognize language Y?
2) How fast can it do so?
When someone says quantum computers are "equivalent" to Turing machines, that's referring only to question 1. In other words, any given language can be recognized by a quantum computer if and only if it can be recognized by a Turing machine.
Just because they are equivalent in this sense doesn't imply anything about question 2. For a concrete example, see http://en.wikipedia.org/wiki/Shors_algorithm -- if factorization takes polynomial time on a quantum computer but exponential time on a Turing machine, it must be reasonable to ask whether quantum computers can be that much faster for a whole class of problems.
Edit: also note that a complexity class is just a set of languages. We can talk about those languages in different contexts, even if they are specified in terms of a particular model of computation.
There are two separate questions: 1) Can model of computation X recognize language Y? 2) How fast can it do so?
When someone says quantum computers are "equivalent" to Turing machines, that's referring only to question 1. In other words, any given language can be recognized by a quantum computer if and only if it can be recognized by a Turing machine.
Just because they are equivalent in this sense doesn't imply anything about question 2. For a concrete example, see http://en.wikipedia.org/wiki/Shors_algorithm -- if factorization takes polynomial time on a quantum computer but exponential time on a Turing machine, it must be reasonable to ask whether quantum computers can be that much faster for a whole class of problems.
Edit: also note that a complexity class is just a set of languages. We can talk about those languages in different contexts, even if they are specified in terms of a particular model of computation.