The best replacement for speedlights is monolights.

The best alternatives to speedlights are rated as following:
★★★★★  monolights
★★★★  strobes
★★★  alien bees
★★★  studio lights
★★  studio strobes

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

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



Google Trends

Scale is based on the average worldwide traffic of speedlights in all years. Click on graph for more.
speedlights
monolights
strobes