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

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.

45's sound better than 33's except when the 45 has mud on it. 45's sound better than 33's except when the listener get reverse 'audioitis'; that's when he can't tell his left ear from his right ear, and good sounds bad.

Anytime I see my favorite music offered at 45 RPM, I am going to buy it.

Dear friends, thank you all so much for the response, and special thanks to anthonymaw, 6t5-gto, chakster, edgewear, shadorne, mikelavigne.... In general, as I got it, with a small margin, the opinion wins that, ceteris paribus, 45 rpm is better. Although, of course, there are a lot of factors ... As for me, the last straw before putting my question on the table was the purchase of Ed Sheran’s Divide - 45 rpm Double LP. The piquancy of the situation was that I wanted to show my 19-year-old son (of course, nihilist with an iPhone headphones), how one of his favourite artists can sound like. The expected triumph was blurred ... I do not think that there is any reason to blame my set up for not being able to reveal all the charms of 45 rpm... Just in case, this is Michel GyroDec, SME 309, Benz Micro SL, Benz Micro phono preamp, Audio Research Gsi 75 and Sonus Faber Serafino. By the way, as a sign of gratitude to all who answered my question, I promise to buy some more 45 rpm 12’’ LPs - with the same content that I already have at 33 rpm - and make a detailed report here. True, I’ll have to wait: I have just ordered these records in the USA, but I live in Russia, in Moscow - and delivery can take several weeks.
Along the way, another question, but to those who have a real experience listening to a Benz Micro SL cartridge (or its heir, Benz Micro Z ). In my country house I have a simpler set (Thorens 350 with Thorens tonearm 92) - and now I choose a cartridge for it that sounds no worse than Benz Micro, but maybe a little sharper (this house allows to listen loudly, sometimes). Can you advise something within $ 3.5 k? Once again, thanks everyone!