What are the different Levels of quality in Power supplies Transformers and Chokes

I am not a builder so my experience is largely second hand.  A local shop builds its own tube electronics--mostly line stages, phono stages, amplifiers and integrated amplifiers.  Many of these custom components are extremely expensive.  For many of these builds, Edcor power transformers (the blue case you mentioned above) are used.  This shop builds stuff largely with price of parts NOT being an issue--sound quality and reliability is what counts.  Edcor makes a lot of transformers, and I don't know which models are favored by the shop, but, they are quite hefty in size.

The power supply is a critical portion of any audio component and the transformers, chokes (if any), capacitors, and regulator (if any) are the critical parts in a power supply. 

There are many types of power transformers (PTs) commonly used in audio such as toroid (donut shape), EI-core (like the Edcor you mentioned), and C-core.  AudioXpress magazine recently had a multi-part series on the different types of power transformers and their properties.  The power transformer must be appropriate to the power supply design (e.g. bridge, full-wave, half-wave, choke or capacitor input, rectifier type) and right-sized for the current demand of the circuit, although many builders have found that the bigger the power transformer, the better the sound.  EI-core are often encased to minimize inductive coupling of noise (hum) with other components and also for looks and protection because they are usually on the outside of the chassis.  Sometimes PTs are potted to reduce physical hum.  I've used Edcor, Hammond, Antek, as well as vintage transformers in my builds with good results.  There are a number of other good quality power transformer manufacturers today.

Chokes can be large, heavy, and expensive, but as @fuzzbutt17 describes, they have wonderful properties that can enhance audio power supply performance.  Like PT, chokes must be appropriate for the power supply design and right-sized for the current and voltage demand.  Also like PTs, chokes are often encased.  I've used chokes from Edcor, Hammond, Triad, Stancor, and Lundahl.

IMHO, power supply capacitors can have an impact on a component's sound as well, although this is a little controversial in some circles.  Generally, more capacitance is better, although the designer has to consider the peak current capability of the rectifier used.  The type of capacitor and it's ESR (Equivalent Series Resistance) can have an impact as well.  Some builders prefer to use polypropylene (PP) in the power supply even though they are more expensive, much larger, and have less capacitance compared to the more common electrolytic.  Modern electrolytic capacitors have much improved properties over their vintage forbearers.  There are many brands of "audiophile" capacitors available today.

Brbrock, I hope this explanation is helpful.