The main ideas behind smaller transformers are:
1. Saturation - (stolen from another forum because I haven't had my coffee yet...) - Saturation is magnetic saturation of the transformer iron. Iron is a magnetism multiplier. When you apply a magnetic field to a piece of iron by wrapping it with a coil with some current flowing through it, the magnetic domains of the iron line up in the same direction as the applied field, and this creates an induced magnetic field that can be around 2000X the strength of the applied field. However, once all the magnetic domains are lined up in the direction of the applied field, the iron is saturated. You can increase the applied field, but you won't increase the induced field (well only slightly). The more iron you have in your transformer, the harder it is to saturate. The type of steel can have an effect too on when it saturates. When the transformer saturates, it acts like a compressor because it can't put out any more volume. It also adds distortion because certain frequencies saturate first.
2. Cost - If you are trying to make an amp or even a washing machine, you have to set a goal of what it cost you to manufacture vs. what you can sell it for. Nobody (almost nobody) is in business for very long without making money.
Soldano doesn't care about cost because they sell their amps for what they want and people buy them.
Mesa tries to keep the cost down to a reasonable level without compromising more than their values will let them.
As for size, the physical size really does matter in a couple of areas.
Number of windings and the amount of iron (as well as the number of laminations in that iron) make a huge difference on headroom.
Basically, the smaller the OT, the faster the amp will overdrive on a clean channel.
The larger the OT, the more clean headroom (less overdrive) you will get on a clean channel.
If you like the sound, then keep it stock. If you need the amp to be louder and cleaner, then a larger transformer such as a Heyboer or Mercury would really open the amp up.
I guess the easiest way to say it (sorry for the rambling):
Fender Princeton Reverb - almost magical distortion when you crank the amp, and very manageable volume levels - tiny output transformer
Fender Twin Reverb - almost no distortion when you crank the amp and the volume can bring down small planes in the immediate vicinity - HUGE output transformer!
