The third version of the InfluxDB database is basically the same core design as Prometheus's third database version which 2.0 uses. I'd expect performance to be broadly similar, maybe a little better with Prometheus as we can take advantage of the characteristics of our domain.
We do have a comparison to Influx on our website: https://prometheus.io/docs/introduction/comparison/#promethe... Which is the right choice really depends on the use case. If you're doing metrics-based operational monitoring, Prometheus is generally best.
Disclaimer: Prometheus developer.