can i move an unit from one battlefield to another if I control both

Not with a Standard Move — a normal unit can only Standard Move Base→Battlefield or Battlefield→Base (Rule 144.4); Battlefield→Battlefield requires the Ganking keyword (Rule 810.1.b).

If the unit has Ganking, yes: exhaust it during your Main Phase in an Open State to move it from one battlefield to the other. Since you control the destination, nothing becomes Contested and no Showdown stages (Rule 450).

Separately, card effects can move a unit battlefield→battlefield with no Ganking needed — e.g. Call to Battle, as long as the destination is a battlefield you control (FAQ #11706).