You could use transitions to do this, depending where the action is.
Place two clips on the timeline directly on top of one another, then make the transition start and end points the same as the clip(s) length.
Try a disolve transition, change the settings so that it starts at 50% of clip A and ends at 50% of clip B (they are both displayed at half strength). If that doesn't work you could try using different wipes, using the same start/end point modification idea, which effectively gives you split-screen the orientation of which depends on which wipe is used. I use Premiere, but assume this can be done in other suites.