What do you hear with a better/bigger power supply and output capacitors in same amp?

If you bridge two amplifiers it will be difficult to tell if the change in sound quality is from the doubled capacitance or the doubled power rating of the xfmr's. However, monoblock amplifiers themselves have no sonic advantage over a single box stereo. The reason mono's exist is for thermal management. It is very difficult to build a Class A stereo amp more than 50 or 60 wpc -- the amount of heat sinking would be ridiculous. To go above that, only mono's are economically feasible. For tube amps, mono's are common because of real estate reasons as the transformers are relatively big per unit of power and need to be separated (magnetic field reasons) and the tubes need space for dissipation. 

Bridging the amps will give you 4X the power from each bridged amp. That sounds like a big deal but it is only 6db louder than the single channel rating of the stereo amp. That assumes that the power supply will handle it. If upgrading an existing amp with bigger capacitors, be sure the wiring to the output devices is 18 or 16 (or more) gauge wire, not ordinary hookup wire which may have been adequate before the mod. Also, at "turn on" the larger capacitors (don't go more than triple the stock values) will pull a lot more current from the rectifiers. Are they up to it?  If using tube rectifiers, may get away with it as they warm up slowly. If your amp has solid state rectifiers, be sure their rating is at least 10 amps. Don't change power transformers unless you really know what you're doing. (Many of my power supplies have 120,000 mfd caps on both the + and - sides of the power supply, so I use 20 amp diodes as rectifiers. Be sure your fusing is adequate. You MUST HAVE fusing. The fuse will not degrade the sound unless you are pushing the amps really hard (like in stadiums).

You can purchase surpus regulated power supplies for under $100 easily, in voltage ratings up to 70 volts or so at 10 amps (700 watts!). Buy two. Use one for + and the other for - sides of the amps power supply. Modest size capacitors (or the original ones) will be more than adequate. Just be absolutely sure the supplies give exactly the same voltage to both + and - sides. I used a pair of such supplies to feed a six channel power amp running 65wpc with terriffic results. Use at least 14 guage wire to feed the amps. By the way, don't allow any magnetic (ferrous) output terminals or wire between the amp and the speakers. I just upgraded the speaker terminals to non-ferrous terminals - big difference! Bare wire or spade connectors give you more contact area than banana plugs. Happy Listening.

I doubled the capacitance in my Hafler DH-200 many years ago.  Most immediately noticeable was that the bass was stronger and dug deeper.  Solo piano had more body.  It was not subtle.

Quiet. That’s the most prominent thing and from that a better presentation, which looks like everyone here may be eluding to. 

Music, not necessarily better