Qubits do not store any more information than bits, it is just that the representation of n qubits requires 2^(n) bits because there are 2^(n) different combinations that n qubits can take.

Qubits "store" just as much information as bits, the primary difference is that qubits have a probability of being observed at both states at once. Consider a 2-level state qubit with state |0> ground and |1> excited. A quantum state can be a normalised linear combination of |0> and |1>. It does not consist of every single state similar to how a pair of spinning D20s does not store all 400 possible combinations.

When observed, the qubit collapses to either |0> or |1> with their respective probabilities depending on the observable. Repeated measurements will only show the same result, as predicted by the Born Rule due to wavefunction collapse. This means that while each qubit holds a superposition of both |0> and |1>, when measured, it will produce a fixed result of length 1 bit.

Such a system produces only probabilistic results, and not definite results from the classical computers we are used to. Quantum computing will make a lot of brute-force algorithms scale better, but it wont replace classical computers, nor provide a universal speedup or extreme amounts of storage. Furthermore, the larger the number of qubits, the harder it is to ensure that all qubits are properly isolated from each other.