LP's... Do they sound better now than 30 yrs ago?

Case by case, record by record. I buy old pressings 10/1 over new ones. I have nothing against reissues or remasters as such; some do actually improve on the early or original pressing (whatever you want to call "original" also varies); some are obviously inferior sonically to early pressings. First pressings aren’t always the best sounding ones either.
I typically buy a reissue when the original is so costly that I’d likely not buy the record at all, given the price.
As to the gear, yes, agreed, we live in an age with more turntables, arms and cartridges than ever. But, some of that vintage gear is pretty killer too- the EMT tables, the refurbished SP-10, Micro-S, etc. I don’t think there is a single answer to any of this. In my case, records I have owned for 30 or more years sound better now than before because my analog front end has improved over time and, with respect to old records, as @lewm and @terry9 noted, knowledge about record cleaning is better and my methods and equipment have improved. (The Monks, which is essentially the same now as it was in the late ’60s does a very good job, as do ultrasonics, with some limitations in my experience, a subject for another thread perhaps).
To come back to the records, there are some terribly recorded, mastered and/or manufactured records from the ’60s and ’70s, just as there are such records today. You’ve got to dig in, trade listening notes with people you trust rather than rely solely on reviews and go through the experience of comparing pressings of records you like. My biggest complaint about audiophile pressings is that for obvious business reasons, the same stuff gets reissued again and again. The obscure, harder to find stuff is often not reissued, or is reissued "unofficially" (read: counterfeit or bootleg) and when it is legitimately re-issued in many cases, it is not by an audiophile label, source material is likely a digital file (not that this is always bad, but...). Occasionally, a good reissue label will do a bang up job on something that is not a warhorse but I think those are exceptions.
To me, this is half the fun of having records- the research, the comparisons, the history behind the recording. The real grief in old records, apart from sorting through the thicket, is condition. That is also a subject for another thread (about which there are already many).

@markmendenhall - there are plenty of threads here and on other fora that sing the praises of US cleaning. I've owned both the Audio Desk and the KL. But, since I'm buying a lot of old records, particularly UK and EU post psych stuff, circa 1967-71 or so, I need the ability to clean out groove grunge that, in my experience, ultrasonic alone doesn't always effectively accomplish. I use US cleaning in combination with a vacuum machine, and for problem records, use a fairly strong cleaner- AIVS #15, followed by a pure water rinse. My next ultrasonic will be a DIY, because it offers more flexibility.  Many of the DIY US adherents get in way cheaper than the made for LP machines, but I'm after the feature set and flexibility. I use a point nozzle type vacuum machine, which doesn't have some of the issues that the more conventional wand type vacuum machines do. Rushton Paul wrote what I think is a seminal article posted elsewhere on this site, synthesizing his learning from a very lengthy thread on DIYaudio on US cleaning machines; he also experimented with filtration, a pump, and chemistry (the surfactant that breaks surface tension of the water and enhances cavitation). Well worth reading in my estimation. 

@markmendenhall - it is less scrubbing, and more agitation. My method, for problem records, is to pre-clean a dirty record first using a mild fluid like the Hannl, that doesn’t require agitation or soaking to remove as much of the particulate matter from the record as I can by vacuum without agitating and soaking. This reduces the risk of grinding particulates into the record that @Inna mentioned.
Everybody has their preference on methods, but I then use a Lloyd Walker applicator, which has a directional fiber to apply the AIVS # 15. I will use a fairly liberal amount, and agitate while the RCM platter is spinning. Then, i’ll shut off the motor and continue to agitate, adding more fluid. My soak times vary, depending on the condition of the record. 5-15 minutes. Eventually, I’ll add even more AIVS # 15 and vacuum it off. Then do a rinse with high grade lab water and vacuum.
The ultrasonic adds a different kind of cleaning and can help loosen some of the stuff that brushing can’t- the bristles or fibers in conventional record cleaning brushes aren’t really fine enough to get into the grooves. Those Disc Doctor/MoFi types are good to evenly apply the fluid but they don’t work as well on the Monks given the speed of the platter and the lack of a clamp. Sometimes, I’ll pre-wash, using the above methods, rinse, vacuum, pop into the US for a wash only and vac dry. If the record is still a problem I will reclean using the AIVS # 15 and will be a little more aggressive --not scrubbing forcefully, but agitating vigorously.
I’m not sure I can say that the results are consistent- some records clean up from distorted to silent players with no groove grunge. Others require little to get them to play quietly. And some are a lost cause. I don’t deliberately try to buy bad copies on the cheap. But some of these records go for well over $500 in "VG+" condition-plays with crackles. A mint copy is often over $1,000. So trying to find something that is closer to mint in condition and cheaper than VG+ with crackles is the goal. These kinds of records are worth the trouble because the reissues generally sound like crap (assuming there is a reissue and are themselves not plagued with "new record" problems in manufacturing and handling).
I rarely encounter a perfect record, but think about it- short of an unplayed copy that wasn’t damaged back in the day in manufacturing or handling, how many 40 or 50 year old records do you encounter that are "perfect"? My standards are high- I don’t want clicks, pops or distortion.
New records, badly manufactured, can have similar problems that often aren’t fixable- non-fill or stitching, where the melted compound hasn’t flowed evenly in the grooves; scuffs, which are sometimes only cosmetic and some that are noticeable scratches- those don’t get "fixed" by intensive cleaning. I can flatten a warped record with about an 80% success rate using a larger Orb/Furutech (some people get great results with a Vinyl Flat for a fraction of the price, but it is, in my experience, a more time consuming process). I get off center spindle holes on new records as well as older ones.
To me, every record is different, and that’s why i’m reluctant to say you’ll go from a 6 or 7 to a 9 on a 10 point scale. A 7 would be unacceptable to me. A 10 (which is the rare bird and is usually an old record I’ve owned since new or the lucky unplayed copy from 40 years ago- not ’looks unplayed’ but actually never played) is pretty rare when you are buying old scarce collectibles. I’ve encountered very few of those.
I’ve had several situations where I’ve bought multiple pressings of the same record simply because the copy doesn’t meet my standards. (Even the Mint- ones are often misgraded or warped).
It is a flawed medium in many ways, but it really does deliver the goods if you get a well recorded record in great playing condition that you enjoy. So, I’m cautious about overstating the benefits of cleaning, but at the same time will confidently tell you that where I have a problem record, I can often improve playback quality by using multiple cleaning methods and repeated cleanings.

@inna - happy to engage in a little experimentation with you; just send me a PM. I am a little unclear about the protocol you are proposing because no two records are the same, and if we are talking about older records that have seen some mishandling, bad past cleanings, etc. they are likely to be markedly different specimens. Shoot me a PM and we'll work something out. 

Inna, that’s fine. Just to be clear, I’m not talking about fixing scratches, it’s more the distortion that you hear when it sounds like the record has been played on a bad record player and the groove noise is high- to the point of distortion. Also, what I call tracing distortion, which is similar- you hear a sort of etched sound from what may have been a misaligned tonearm/cartridge (crystal needle anyone?) from a kludgey old fashioned record player. Sometimes, not always, those kinds of distortion are just a result of crap in the grooves that has been cemented in and it isn’t easy to get it out. Thus, the maniacal cleaning regime on seriously scarce copies. If it is a cheap record, I often just replace it if a couple of cleanings don’t do the trick.

Every used record has a story. We just don't know what it is.