That's a loaded question, but here is my take as someone who works on them every day, and has owned quite a few. I'll stick with the 4 cyl cars. It really isn't all about the engine itself, either, but somewhat the platform it was found in.
The first TDI we got... the B4 Passat, was a great all around package, even if a bit (or really, a lot) dated when it came out. Last gasp of the oil (since 1974) original Audi engine design. Not super complex, or cutting edge, but pretty simple. Pluses were simple 3-box design sedan rolling on a long wheelbase, very roomy interior, and a wagon version to boot. Incredible range, and really nothing at all of that size at the time could compare. Downside was, for 'murrica, no automatic option available. Granted, the 096/01M is a pretty bad transmission, especially back then, but I think they may have sold a few more of these had they had one available.
The A3 Jetta, which had already been out for a few years, arrived a year later with the TDI option. Pretty much a scaled down version of the same basic car, but we didn't get any wagon option here, and again no automatics.
The best thing about these early TDIs was the value they represented. They were about a $1200 option over the base ABA 115hp 2.0L gas engine (which was dropped from the B4 halfway though the 1997 model year). And with that, you also got the beefier cable-shifted 02A transmission (the ABA still was bolted to the ancient rod-shifted 020 box from the '70s). Everything else was the same. Same trims, same options, same radios, same colors, everything. So other than the $1000 option to have the transmission go TU at 80k miles like the gassers did, you could essentially buy a better engine and transmission in the same car for only $1200 more.
These engines had some limitations, the pre-ULSD days meant intake clogging, and the EGR valve was integral with that intake, making cleaning a royal pain, and a NEW intake very expensive. They also suffered from crank snout failures due to the increased load the higher pressure rotary pump placed on it versus the old IDI engines. The A3s were still employing drum brakes in the rear (although that design was tried and true and worked well, to be honest). The A3 Jettas also got fold down rear seats, like the Golfs, something the A2 Jettas didn't have (just the "ski boot" hole... if you know, you know...
).
Like most platforms, when one has been around a few years, lots of kinks get worked out, and certain improvements emerge. Given these TDIs appeared at the end of these platforms' original cycle, I'd say they were probably a bit better than the ~1994-95 cars. But still, being based on the 1985 A2 platform, they were pretty dated. Lots of their electronics and systems were sort of kluged on, the wiring in the dash looks like a rats nest, with random connections just "floating" in places, and in some cases still using vacuum actuators on some things. It really was time for a fresh start.
That fresh start began with the 1998 New Beetle, which was based on the all-new A4 Golf, although we wouldn't see that Golf (and its sedan version, the Jetta) until halfway though the 1999 model year. But with that '98 Beetle, we got an all-new engine family, that (my opinion) took the best of the basic design Audi previously had, which was certainly good, and improved upon it and made it better. Gone was the intermediate shaft spinning in the block, which was a vestigial leftover that used to run the gassers' distributor, mechanical fuel pump (to feed these awful things we used to have called a "carburetor"... look it up..... ugh... ), or on the diesels, the vacuum pump (when equipped with power assisted brakes... there actually were older diesel A1 cars sold that had no such luxury).
Curiously, these new engines in diesel form kept a revised version of the old injection system. The sturdy, simple, tried and true Bosch VE style pump. But with a much improved method of setting and tensioning the belt and the timing, and [eventually], a much longer service interval. A new variable nozzle turbocharger, etc. The mighty ALH... the only 'new style' VE TDI ever sold here, with its meager 90hp and 155tq, I think will probably go down in history as being the favorite for us. Nearly indestructible, efficient, easy to service, easy to tweak, easy to understand, easily THE simplest engine management system on any car sold here since the '60s (if you are able to avail yourself of the car's great Bosch EDC15 system).
And the car that the ALH was bolted into was a nice fresh start, too. Overall, I find them easier to service a lot of things on, they have a cleaner, simpler, more logical layout of a lot of their systems simply because they were actually designed to have them, it wasn't something that came along later and got added. They learned to streamline and make modular the front end, so it comes off super quick and easy. A must for VR6 cars. Completely revamped powertrain mounting (which is now pretty much the industry standard, most every modern transverse powertrain is arranged the same way). Standard disc brakes all around. Composite battery tray instead of the rust-prone metal one. OBD for all the major modules, with a lot of nice bidirectional access. In other words, a gold standard for a small car, and if you got the diesel, you got a great engine as well. Plus, they were still reasonable... a ~$1600 option, and while that was more than previous, and the base gas engine also got the newer transmission this time around, you still had all the same trims. If you wanted a complete optionless Golf but with the TDI, you could get it. And, if you wanted to curse yourself, you could also for the first time here get one that shifted itself (and eventually would **** itself) for $1000. Which, again, 'murrica, is pretty much a must for some people. It does suck that the 4sp 01M clearly wasn't up to the durability of the rest of the car. But I guess even the fanciest of underpants can get a skidmark now and then.
The later A4 cars got the PD engines, which had already been an option in Europe since late '99 on some models. I like these, I think there is a lot of unwarranted hatred of them, but my take is that they are not nearly as bad as many are led to believe, and while they do require a bit more careful care of some things, they can prove to be quite reliable and durable. The trade off was more power with less fuel efficiency, and better "emissions" which is its own can of worms. Best part here is, if you wanted to forego the clutch pedal, the optional automatic became the 5sp 09A which was supplied by Jatco and while it certainly is no manual it is a FAR better unit than the old 01M and is also far less of a hit in power and driveability. I own a 2004 Golf with one, and it is plenty peppy around town, zips down the highway happily into the illegal side of the speedometer and would happily run fender-to-fender with my stock manual ALH Golf. And at 223k miles, it is reliable and solid. Plus, these later A4 cars also enjoy all the final improvements granted to that platform. Things like better radios, lifetime cupholders, better ABS/ESP systems, etc.
