The best replacement for softboxes is umbrellas.

The best alternatives to softboxes are rated as following:
★★★★★  umbrellas
★★  octaboxes
★★  shoot through umbrellas
★★  umbrella lights

Your alternative for softboxes is not listed? Suggest!
Speaking about softboxes, one probably shouldn't forget about speedlights.

Other search terms related to softboxes and their ratings are:
★★★★★ speedlights
You have in mind a companion for softboxes and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of softboxes in all years. Click on graph for more.
softboxes
umbrellas
octaboxes