The Weeping Angels move incredibly quickly when out of sight, so maybe in this implementation, they could be a subplane life-form that’s able to teleport at will, but only if nothing’s looking at it when it teleports. They can teleport about 6 squares in one move, and if they appear adjacent to you, they can attack.
That way, they’re easily outrun if you encounter them in open terrain in daylight, but if you’re in an enclosed urban or forest area or indoors, one could catch up with you in moments if you lost sight of it around a corner.
As for the nature of their attack, how about something like this: They feed off energy in whatever form is most readily available, targeting one of the following - either in a set order of preference, or at random:
[ul][li]Every Plutonium Cell you have, including the charges in your Advanced UPS.[/li]
[li]Every battery you have, including those in battery-powered devices.[/li]
[li]All the stored power in your bionics.[/li]
[li]All the readily-available metabolic energy in your body, leaving you at an extreme level of starvation.[/li][/ul]
A successful attack will also leave you with Teleglow.
A single attack will tend to leave the Angel satiated for awhile, and they’ll let you leave, but they may track you by starting to teleport after you once you’re out of sight.