A large part of what you're listening to is efficiency-related. Wattage is actually meaningless (stay with me), it's about Sound Pressure Levels. Loudness is a function only of SPL, not of wattage.
A typical guitar speaker is 100dB efficient, with about 10 watts, you're moving along at about 112dB, near the threshold of human hearing damage. To produce that from a home speaker that is 88db/W, you need about 200 watts, and a lot of home speakers will not even hit that, because of the second limitation.
The second limitation is frequency response and excursion. A typical 15" Pro woofer will reach down only to about 50Hz, and the excursion is limited to about 3mm. This still lets the woofer hit destructive SPL with under 30 watts of input, with full response down to the specified 50 Hz. A typical home woofer is run without filters and is expected to reach to at least 40Hz, and due to WAF is not supposed to exceed 7" or 8" in size, most stop at 6.5". This means a large excursion to hit the low-end output, some home woofers have about 10-15mm one-way excursion. At levels above 105dB, the required excursion from a 6" diaphragm is around 25mm, maybe more. It's just not feasible to derive any low-end output at that volume level.
Basically, if you have a home woofer trying to push 40Hz at 105 dB, it will damage itself through excess cone movement. This may lead to the tinsel leads snapping, the coil popping out of its gap and the spider tearing. Not nice things, and we can generally hear these things happening long before actual damage happens, so we turn the volume down. The good news is that the threshold of pain is about 100dB for most people, so the requirements can be toned down.
Obviously the last factor is the space itself. Pro speakers are typically used in large or outdoor venues, where a higher SPL level is required to cover the entire area. Most of the time we never use those volumes at home or in home systems, so it always seems outdoor speakers are louder.
In short, it is more to do with the speakers than the amp.
Guitar and bass amps are pretty different. They are usually meant for studio or small venues, with live venues requiring head-and-cab arrangements. A Marshall stack can be 100 watts and employ 4 12" speakers, enough to blow the windows off your house. In large venues they will get secondary help from the PA system as well. Bass when played at venues usually goes direct into the PA along with everything else, with the guitars having their own heads/cabs. Live sound is a slightly different ball of wax, so won't get into too much detail. It uses super-efficient speakers and medium-power amps, though power is cheap nowadays so it's not uncommon to see more linear speakers and 1000-watt amps in a typical FOH system.
