Having been involved with several FAA STC's for GA and airliners I can pass on my experience. Additional FAA information is available in FAR part 21, 23, 125 and here.
First, transport, airliner's, etc are not held to the same rules. The FAA generally considers the engineering department of aircraft manufactures such as Cessna, Boeing or Aerobus to know what they are doing and pretty much rubber stamps anything they come up with. What they are mostly looking for is performance and operational documentation.
[ For 5yrs I was part of a Boeing team that primarily modified doors such as cargo doors for special purposes. We installed and verified or corrected engineering drawings for the modification and approval process. FYI: when I wasn't doing that, I did the final ramp, taxi and opps check of aircraft before their first flight out of Everett WA.]
GA aircraft STC's are administered by the regional FAA office (FSDO) and the process is highly dependent on the region and personal inspector. (The FAA says it's standardized, but it is not.) For example many float planes are flown all the way to Alaska to get approvals because the Anchorage regional office is experienced and generally more permissive than other offices.
Typically the FAA reviews the applicant against new product standards and expects the applicant to provide the "same as" level of safety found in FAR part 21, 23, and 125. With the new "industry self policing" policy passed last year, all bets are off on how it will be done in the future.
I have seen STC's approved with as little explanation as "performs equal to or better than original equipment..." on high performance Alaska Borer props, vortex generators, lights, antennas, gauges, etc with very little or no other data. In 2000, the Alaska FSDO changed from pencil whipping strobes (i.e. ...it works fine on 3000 other Cessna 172's..), to requiring 3 page form that includes a illumination profile chart to be filled out! The A&P's started a revolt and I don't know what happened, I moved three years later to work for Boeing in Seattle.
EXAMPLE: I assisted an Alaska company in a fuselage battery mount. I took a damaged C-180 and removed the tail surfaces and separated the fuselage aft of the cabin. I then hung a 25"G" horz weight (later 7G vertical) from the battery CG for 5min and took a picture. I certified the test and submitted it and received approval. I then took that approval and resubmitted approval for all applicable aircraft with the same skin thickness (individual W&B was calculated for each installation). It took about 6mo for the first approval and an additional year for about 15 additional aircraft to became STC approved. The company estimated it cost around $20-30k.
It often depends on the whim of you local FSDO. One of the reasons Wichita Kansas is a popular place for manufactures is the FSDO office is notorious for ignoring FAR regs. A good example is one FAR says "...every part large enough to be identified must have a unique part or serial number". Try to find a serial or part number on control columns/sticks, rudder peddles, flaps, wings, ribs, bell-cranks, etc. There are AD's on Cessna parts such as gauges but they don't have a part or serial number! An A&P can't write, I complied with the AD by replacing part "x" with new part "y"! (what some A&P's do is use the parts manual number, but the parts manual is not "approved" data by the administrator.)