Sorry but you're either complete moron or you have not played Fallout.
There was NO realtime/CTB mode in original game, thus to move you had to spend 1 action point per hex moved (and if you had your leg crippled it was 3AP per hex IIRC).
Again this is what it means for realtime if realtime is supposed to play the same as turnbased/original:
Action Point would be defined as AP=Actions/Time. Time is in turns, actions are various - so for example 1AP might be 0.2shots per one turn, or 1 hex per one turn.
Now in realtime there is no such thing as turn, but it still uses rules from turnbase game, so developers might state that for example turn passes every second in realtime. That would mean every second your action points would regenerate (that means for 10AP build, it would be 1AP per 0.1s, for 20AP build, it would be only 0.05s per AP).
But every regenerated AP is still action per time - what was previously 1 hex per one turn, will now be 1 hex per one second, for 10 AP character it would mean 10 hexes per second, for 5 AP character only 5 hexes per second, for 1 second turn that is.
Currently however, you receive nothing when you are moving, no matter how much action points do you have. That means in former case everyone would move say 10 hexes per second. So obviously, builds with more than 10 action points would have disadvantage in realtime mode, while those with less than 10AP would benefit from realtime.
Regeneration makes less sense, because it addresses only a part of this RT/TB mode parity. That means if you regenerate or spend AP when moving, you allow characters to do the same actions per time in RT, but do not grant them positional advantage when they 'use' all their AP on moving.
But still, imagine again situation where turn is 1 second. Now character with 10 AP would be considered neutral for example (but ideally it would be the lowest amount of AP you can have, see later). If he moves, his action points do not regenerate. For character with 20 action points, regeneration would take those default 10 action points, and he would still regenerate 10 action points per turn (that is in this case one second). That means per one turn he could shoot twice and move 10 hexes. While the other guy could either move 10 hexes or shoot twice. Now anyone with less than 10 action points would need to lose the missing amount of action points per second of running (eg if he has 5 action points, after the second of running they are all drained, and he must stop, otherwise he would be performing more actions per turn than his action points would allow).
Bonus movement would still work, because for example guy with 10 AP and 2 extra movement points would regenerate 2 action points per second when moving.
And last thing. It's just retarded to balance around anything else, because that way it will ALWAYS alienate TB rules to RT mode.
It is NOT possible to implement sequence realtime without stopping players for a while, and would be probably better to remove it from TB as well by making TB turns simultaneous (eg. every player in turn based would play at once, but once they spend their action points they cannot play until every other player ends turn as well).
EDIT: by the way to achieve perfect balance between TB and RT (without sequence), action points would need to be REMOVED from RT (instead shooting would take some time before it's completed, so while you spend 5 AP on your shot, your enemy can travel 5 hexes), but as far as I understand engine is still kinda limiting in this aspect.