Does AES-NI offer better side-channel protection compared to AES in software? Does AES-NI offer better side-channel protection compared to AES in software? Also, it would be great of you could provide according references in your answer.
Yes, AES-NI was specifically designed to be constant-time and thus offers better side-channel protection than (some) software implementations. Note however that these day there exist quite fast side-channel resistant software implementations for AES, which are in-use by the better crypto libraries. AES-NI mainly offers a speed advantage over these implementations.

From the Intel® Advanced Encryption Standard (Intel® AES) Instructions Set Whitepaper:


  The AES instructions are designed to mitigate all of the known timing and cache side channel leakage of sensitive data (from Ring 3 spy processes). Their latency is data-independent, and since all the computations are performed inter
  nally by the hardware, no lookup tables are required. Therefore, if the AES instructions are used properly (e.g., as in the following code examples) the AES encryption/decryption, as well as the Key Expansion, would have data-independent timing and would involve only data-independent memory access. Consequently, the AES instructions allow for writing high performance AES software which is, at the same time, protected against the currently known software side channel attacks