Yes, all modern symmetric ciphers strife to offer (approximately) x bits of key strength for an x-bit key size, just like AES. If they don't, we presume they are broken.
Although there have been attacks on Salsa / ChaCha using fewer rounds, it doesn't seem that any attack has reduced the bit strength of the full cipher. Furthermore, differential cryptanalysis doesn't seem to make a dent in the security claims either.
The best attacks on AES ever so slightly bring down the security of AES to something near 126.2 bits. Also, attacks on ChaCha seem to be over fewer rounds relative to the total number of - but it is unclear if that tells anything about future attacks on the full cipher (if any).
So you could argue that a 128 bit ChaCha20 may be ever so slightly more secure when it comes to the algorithm itself.
Generally ciphers such as ChaCha20 are also less prone to side channel attacks, but if and how much they are susceptible is implementation specific (and system specific) in the end.
Note that I make these claims using Wikipedia as source (see further below for the ChaCha variant), so you may want to verify the source material and look for more recent developments.
Some ciphers modes like SIV mode do not play fair and indicate a combined key size for encryption and authentication. In that case the encoded key size doesn't represent the key strength.