Just for looks?

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"?

Thanks.

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.