I connect mine using a USB-C to HDMI cable on a monitor that only has HDMI and DisplayPort connections. The bigger hit on performance isn't the connection itself, but the resolution of the external monitor. A QHD or 4K monitor would have a bigger performance hit than FHD (1080p) monitors because of the integrated videocard having to drive more pixels.
The biggest benefit of a USBC monitor vs HDMI or DisplayPort is that a USBC monitor may supply power to the MBA, and may also serve as a USB hub, thus giving you a single-cable-docking solution of sorts. Specifics of course will depend on the monitor.