Considering the OPs question and criteria, "biggest and most rugged," I think the clear winner would the the North Cascades in Washington.
The volcanoes there start close to sea level and rise to close to 11k (Baker, Glacier Peak) giving the "range" more elevation gain from base to summit that other peaks say in the Tetons, Rockies, etc. So that is how I'd quantify "biggest."
In considering criteria to evaluated "rugged," I think of developed trails, or lack thereof, severity of bushwacking, steepness of terrain, complexity of terrain (rock, snow, ice, elevation gain and loss, river crossings, etc.) I have yet to set foot in a range that I could say, when taken as a whole, that offered a bigg ass beating that the N Cascades. Some corners of the Sierra and places like the Sawtooths, and Absorkas come close, but overall the cross country travel is easier, the climate more fair, and there are more developed trails and routes than the N Cascades.
I mean the place has it's own bushwack rating system for crying out loud:
In his description for a route on the venerable roadside test piece, Mount Index, the legendary Fred Beckey recommended imitating "a gorilla through the brush" to navigate difficulties when approaching the actual hard part, climbing the mountain.
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Of course the N Cascades would hardly occupy a small corner of the trailess alpine wilderness that is the Alaska Range, but we aren't allowed to talk about that here.