Yes, both CumulusMX and Weather-Display have FTP capability. Both have multiple templates available.
CumulusMX does not currently use a METAR for sky conditions, but the CU-Plugin for the Saratoga template (and also the Leuven template) add that capability. Weather-Display can natively use a METAR (in conjunction with a solar sensor) to produce sky conditions/Icon.
Both CumulusMX and Weather-Display produce near-realtime (5 or 10 second) update file and the Saratoga and Leuven templates can use that for more rapid updates on current conditions to your website.
Weather-Display has the most features, and because of that, it may also have a slightly more difficult configuration initially.
CumulusMX uses a local website for customization and has fewer configuration options for an easier initial setup.
You can see what the Saratoga template with Weather-Display looks like
here and with CumulusMX
here BTW, I've been running Weather-Display since 2004, VWS since 2007 (for template testing), Cumulus since 2011, CumulusMX since 2015, and WeatherLink since 2004. My main site uses Weather-Display (and a bit of WeatherLink) for displays. The other software continues to be used for live testing with my template sets.