Do 45 rpm 12" LPs really sound better than 33 rpm?

@newf27 definitely, those 12 inch 45 rpm promotional singles from the golden era of analog are the best, made for radiostations and deejays, and you’re right that these are the first that comes from the stampers. In my opinion they are unbeatable by any 180g or even 200g reissues on the modern days.

I am a huge fan of Analogue Productions 200gram reissues. I have most of the Verve reissues remastered by George Marino and these are only available in 45rpm and are some of my favorites, they sound spectacular. But I also gave a decent number of their 33rpm 200gram reissues and when given the choice (like Pet Sounds or Time Out) that are available at both speeds I choose the 33rpm every time. They sound unbelievable and if the 45s are that much better it is hard for me to hear and I would rather not do all the flipping. I have the Son House and Muddy Waters Folk Singer in 33 and both are offered in 45 and I was fairly convinced I liked the 33s more.
That being said, the Mofi One Step of Bridge Over Troubled Water is 45 and I am not sure if that helps make it so incredibly good or if it the pressing and remastering that makes it so awesome? 
All being equal the 45 might be slightly better but I'll get up once per album rather than 3 times given the choice 

It’s a compromise between dynamic range versus playing time.
When a record mastering engineer cuts the the stamping master, he has to limit lateral cutter stylus movement while maintaining adequate groove spacing which in turn affects the amount of play time on the record.
The RIAA equalization curve was originally invented to reduce the bass frequency amplitudes during mastering  (and emphasize the treble frequencies) exactly for this reason so that on playback with the reverse equalization you get "rumble" noise and almost non-existent hiss noise.)
Dynamic range compression is often applied in order to fit more music onto a side of the record.
If the engineer can cut the record with less playing time per side (i.e. a 12 inch record with only 3 songs instead of 5) then he can afford to allow greater lateral cutting stylus movement and thus greater dynamic range but only up to a limit before it can potentially skip on some record players (hence the evolution towards high-compliance light tracking force needles).
A great example of this was Led Zeppelin II LP there is a now rare and highly-sought after commercial "hot" print with very high dynamic range but it skipped on some record players and got recalled and was remastered with lower dynamic range and better trackability at the expense of sound quality.
At the opposite extreme were those 1980s K-tel compilations records where they could fit 8 to 10 songs per side but they sounded flat like AM radio due to extreme dynamic range limiting to maximize playing time.
The 45 rpm speed will minimize the phenomenon of "inner groove distortion" since the groove speed as seen by the needle slows down as the record plays from outside to inside. It’s caused by the cutting needle physically deforming the track behind it because the groove speed is too slow and has been a known problem since the 33 RPM LP was first invented and one of the reasons the first records were cut at 78 RPM.
Spinning the record at 45 PM practically eliminates inner groove distortion and on a 12" disc it’s mostly using the outermost track area with the highest available groove speed.
Of course the down side is that you have to flip the record over more often which *IS* distracting.
Personally I happen to think those 45 PM 2 disc 12 inch re-releases don’t’ make sense!
For my money if I really cared about maximizing sound quality I’d just buy the CD release - no need to deal with limited dynamic range, surface noise or the need to interrupt the listening experience to flip or change the record - just pure music enjoyment.
Besides many vinyl records are cut from digital master tapes now unless they say specifically that it was cut from the original analog 30 IPS studio master tapes.

I have done a number of 3 way tests on 45 vs 78 vs quality CD recordings. The 45s always come in last. In fact on my system, a top end system, they just sound "bad" when compared to the 33 LP.  To me it is just a gimmick to sell records. 

Your “tests” prove nothing that anyone else can use for guidance.