Depends if your license uses Dem units (new license model) or Rum units (old model).
For DEM the activegate check (simple http request) is 0.1 DEM per check.If you have RUM units, you are out of luck AFAIK and you can't use this functionality until you migrate the license to the DEM model.
From the licenses point of view (and also from the cost) there is no difference. Http Monitors are priced per Synthetic web request. Please take a look at: https://www.dynatrace.com/news/blog/the-next-gener... as Dynatrace classic synthetic ("Backbones") will be retired by 31. October 2019.
You can also take a look at our Synthetic monitoring upgrade center: https://community.dynatrace.com/community/display/CLASSIC2SYNTH/Synthetic+Monitoring+Upgrade+Center