What makes the advancements "minor"?
We don't get any qualitative information on anything except perhaps the warp factors, and that's contradictory anyway. Weapon power is undetermined - in ship-to-ship, it's undeterminable, even. Transporters do weirder things in TNG era than in TOS era. Sensors pick up things they didn't pick up in TOS, mainly because there are more lines to be impregnated with technobabble than before.
Would the difference between the 19th and 20th centuries really be more noticeable than the difference between these fictional 23rd and 24th?
Timo Saloniemi
Put it like this... the difference between the 1940's a and 2012 in real life is effectively 72 years... for TOS vs TNG, its 75 (at least to the Dyson Sphere episode) which is close enough... even though we had plethora of technologies available to make big changes in the early 20th century (for example creating material abundance for every person on the planet from landfills and switching over fully to geothermal power in 1911 - both of which would need about a decade or so, and making vertical take-off and landing aircraft controlled via electrodynamic means (also noiseless), while from the 1950-ies onward using solar, wind, wave and tidal in such quantities that together they form loads of energy we wouldn't even know what to do with, along with mag-lev trains from 1974, space based solar power since 1985, etc., etc., etc. ), but things are basically the same apart from having Internet, more powerful computers (outdated as they are with persistent use of silicon as a base material instead of others that were viable since 1997) and revised cars (EV's could have easily been used since 1990's on mass).
Problems in real life are related to the notions of profits/money which inhibit our technological development (high efficiency and designing things that last and can be easily updated would kill profits because the current system requires cyclical consumption/planned obsolescence in order to keep the money flowing continuously resulting in products that last a small amount of time, cannot be upgraded, are revised at best even though we could be seeing huge leaps)... whereas in Trek, the writers wanted to stick to an outdated mentality... redressing TOS and making minor improvements here and there, essentially sticking to the notion of relative stagnation with little changes - even Geordi mentioned to Scotty that the technologies used in TNG are not that different from the TOS ones - impulse engines being one, Warp speeds being revised and faster (albeit if TOS and movies would have us think specifically, the Feds essentially regressed backwards severely) - essentially, the basic technologies are still alive and well - in improved form. Did we suddenly forget that the Federation has the brain power of 150 different planetary cultures, doesn't use money and is mostly motivated by the notions of self-improvement? Well, humans are, but this mentality would probably spread very fast among UFP members once they see how efficient it is.
Transwarp seems to have been conveniently kicked into the curb (and Warp was already fast enough to transport The Enterprise-A thousands of lightyears to the galactic core. Heck, the Warp in early TNG was also very fast (faster than Kirk's... but it was reduced in power/efficiency by the time Voyager rolled out).
People often say that Roddenberry was a nutjob for wanting to implement his own original ideas into TNG (exploring other galaxies instead of the Milky way), and then of course much more liberal social life in terms of sex and other things - I say that people are a bit limited for shunning his ideas (which were more in line with exponential increase in technology - but American TV...).
There has been a much larger tech development in Trek since the WW3 era to Archer's time - such as humans catching up to the Vulcans (or getting very close to them) in mere 90 years... then they probably closed this gap by the time the Federation was founded, and post Federation creation (with Tellarites, Andorians and Vulcans collaborating with Humans)... the explosion of ideas, technologies, etc. would have been orders of magnitude higher than ever before, and kept increasing with new races coming into the mix by working together.
In short, Trek was severely gimped because they wanted to keep the show 'relate-able' - which in my opinion is completely absurd as Trek was initially trying to challenge preconceived/established notions that happened in real-life.