Just for looks?

I've noticed several manufacturers design very large and heavy amps with large transformers and huge capacitors. Specifically I've seen the insides of a Carver amp and Aragon amps.
Can someone explain why at the same time other manufacturers build higher end, more expensive amps that are much smaller? I recall seeing a Conrad-Johnson that appeared very thin, and very expensive.
All things equal, the larger the power output of an amp (e.g., 30 watts compared to 100 watts -- assuming the same kinds of watts measures are used), the larger the power supply transformer and power supply capacitors need to be. The power supply pretty much dictates the output wattage since that provides the limit of amplification (not a super accurate description, but I hope the point comes across).

However, all things are not equal. There are also different designs of amps and those designs differ in efficiency. Generally, the less efficient amp designs (class A) yield a potentially more accurate reproduction. Of course, a very good class B design (more efficient) could be preferred by many to an OK class A design.

Lest you start believing that less efficient large wattage amps are the way to go, bear in mind that many prefer very low wattage designs which drive very efficient speakers. Typically, these are tube amps, but they don't have to be.

It's very difficult to be accurate with generalizations. The point is that very small amps can sound very good and very large amps can sound very good. One may provide a more liquid mid-range while the other may provide more bass slam. Size only matters relative to your particular needs and preferences.
Like large speakers and small speakers... neither is necessarily better.

I had a nice NAD in a slim case at 40 Watts - was great.

Still wondering a bit, however -
If I were to compare two amps side by side each being 100 watts and one was thin and the other HUGE - how is the thinner amp with smaller transformers and caps performing relative to the larger amp assuming both are "Hi-End"?

mg2am, all things equal, I would always go with the more robust power supply. But again, a very well built class B design in a thin case could indeed sound better to you than a huge amp with a huge power supply. Let your ears decide.
Size does not matter. A handful is still a handfull.....

I am inclined to think that it is how any given amp-regardless of design or appearence, matches with the speaker of your choice. Certain aspects of a amplifier may seem preferable on paper or by appearance, but the real telling is when you hear the results of that amplifier with your speaker.
Amplifiers with large caps and transformers are generally designed to deliver more current to a power hungry, high wattage output stage but this alone does not equate to good sound quality. However there are certain applications that require this high power, high current, like power hungry speakers. Many audiophiles feel that amps rated more than 100 watts per channel loses the sweet spot. The main reason for this is because higher wattage amps require more electronics and output devices. The more electronics a signal passes through the poorer the sound quality. A case in point is most audiophiles prefer the sound of the lower powered McCormack DNA 0.5 (100 watts per channel) over the higher powered DNA-1 (185 watts per channel). The ideal strategy for any engineer in designing an expensive high end amp is to keep the signal path as short as possible and use the highest quality parts, this is why a small high end amp can be so expensive, your paying for engineering, design, & parts quality.