This matches my experience. With a Gigabit Ethernet connection, I find it very difficult to distinguish a desktop streamed via Parsec from a local one. RDP is noticeably laggy in comparison. I would even say that Parsec over a good internet connection (a few 10 MBit, ~10 ms ping) feels more responsive than RDP over LAN.
What I don't like is that Parsec relies on third-party servers for the session initiation, and that streaming Linux desktops is currently not supported. Maybe the open source implementations of Nvidia's GameStream (Moonlight and Sunshine) could be an alternative.