Shor's algorithm works fine for the Elliptic Curve Discrete Logarithm Problem (ECDLP)[1]. So it'll break ECC.
There's no indication that it can be used to break several other types of problem that can be used in asymmetric cryptography. These other problems are less efficient and have different trade-offs (some have huge keys, some have huge outputs, some are really slow) and picking appropriate parameters to make them usable while still being secure is a difficult problem. Solving that is the aim of NIST's post-quantum standardization effort.
There's no indication that it can be used to break several other types of problem that can be used in asymmetric cryptography. These other problems are less efficient and have different trade-offs (some have huge keys, some have huge outputs, some are really slow) and picking appropriate parameters to make them usable while still being secure is a difficult problem. Solving that is the aim of NIST's post-quantum standardization effort.
[1] https://crypto.stackexchange.com/questions/51346/shors-algor...