Signing and encrypting are not interchangeable: they have different purposes.
If you need authentication of a user or a service, then sign. If you need authentication of data, you can sign it or use a MAC (message authentication code).
If you need confidentiality, then encrypt the data.
If you need both authenticity and confidentiality, you have to encrypt the data then sign (or mac) the encrypted data.
Performance-wise, symmetric encryption usually use the AES-NI instructions of the server's CPU, which makes this operation extremely fast, oftentimes it's not even noticeable over the transmission delay.
Asymmetric encryption/decryption needs to first encrypt/decrypt the symmetric key, before encrypting/decrypting the data. This encryption/decryption of the symmetric is roughly equivalent to a signature operation.
Signature and asymmetric encryption are comparatively much slower than symmetric encryption. Depending on the algorithm used, its impact can be quite noticeable. Depending on the algorithm used, MACs computation can be hardly noticeable, for example in the AES-GCM algorithm, or they can necessitate a second pass on the data and double the encryption time.