NOT a crap shoot.
Correctly engineered the 45 will always sound better because the higher speed enables more faithful recording of the music. Compare with reel to reel tape - 7.5ips is better than 3.75 and professional studios often used 15ips. Some of those recordings remain the best masters we have.
Consider - an LP should not contain more than around 20 mins music per side. More than that requires compression of the grooves which reduces dynamic range (but look at the brilliant job Decca did on the Stones' 'Aftermath' that runs 52+ minutes) . Do the maths - cutting less than about 9 minutes on a 45 side allows the engineer to cut at a higher level without crashing the grooves. But if you try to cram more than that, then the advantage is gradually lost..
I bought a lot of used 45s in the 80s and 90s, mainly 70s and early 80s rock. As others have posted, many of these are the best sounding vinyl I have. A particular favorite is Frank Zappa's Stairway to Heaven b/w Ravel's Bolero - both outtrageous over-worked parodies of the originals. I also have singles by most of the 80s big names.
@emrofsemanon If some of your 45s are noisier, it is because they are dirtier, or perhaps they were played a lot or mishandled by a DJ in the day.