Would you say Mauna Kea (base at sea level with a peak of 13,803’) is smaller than some mountain with a base at 9,000’ with a peak of 14,000’.

Some people point to prominence, but that is often a garbage number as to determining how big a mountain is. Prominence is measured to the saddle that connects that summit to higher terrain. That would put Mount Elbert’s starting point for prominence somewhere in California with the higher terrain being Mount Whitney. Elbert is definitely not 9,000’ (its prominence) base to peak. It’s closer to half that.

Yes, Utah mountains are “big” base to summit, often more so than Colorado mountains.