Adobe Edge Animate is a much different tool from Flash, though there will be inevitable comparisons between the two. Also, keep in mind Flash as a product has been around for over 15 years whereas Adobe Edge Animate is much newer and just coming out of preview release.
That said, part of the reason it is missing some of the features of Flash is because they should either be done in another app such as Illustrator or Photoshop, or they don't directly pertain to the workflow using HTML5, CSS and Javascript/JQuery. Flash had more tools built into it for drawing vector shapes, Edge Animate assumes you are creating your graphical assets in another program and importing them instead. What little you can draw in Edge Animate are not your standard vector shapes, they are actually just HTML DIV's being styled with CSS. Flash is frames based animation, Edge Animate works off of timelines and moves things around with Javascript and CSS transitions. In Flash you would draw every frame one at a time (unless you used their tweening tools). In Edge you start with point A on the timeline then further down point B and it will auto animate from one end to the other - a different workflow.
As far as stuff like Actionscripting, I'm under the impression Edge is assuming stuff like that is already being handled by Php. You can open an existing web page in Edge Animate and animate sections directly, which you can't do in Flash.