I love these questions! Lets start off:
2005.5-2007 is a BRM 1.9 TDI. 100hp / 177 ft/lbs of torque
-Slight changes from the previous BEW(2004-2005.0) but no real power increase, just mainly emission decreases, and a more efficient turbo.
-All BRM TDI's are plagued with bad camshafts, they will need to be replaced along with all the lifters at one point, so make sure that is done, or make it be reflected in the price.
-EGR valve leaks are common as well, a notable hissing noise at idle and especially when the engine is under load. If you send it to a shop it'll be a roughly $900 fix
-Otherwise, bulletproof engines
-A little lacking on power at higher speeds
2009-2014(CR EA189 2.0L TDI) 140hp / 236 ft/lbs of torque
-These engines are all the same across the board from '09 to '14.
-High Pressure Fuel Pump issues are the main concern, a difficult DIY once it fails, VW charges around $7,000+ to fix as the injectors, the tank, lines etc need to be replaced. It can go at anytime, usually within warranty as premature failure is common. Some members have 200k+ with the original HPFP, but some also have 20k and have had theirs replaced already. The 2009-2010(MK5) years were the most notorious for these failures, VW seemed to have ironed the issues out at around 2013, however some still do fail on the newer cars
-*Water in intercooler*, removing the bellypan and loosening the clamp on the inlet side of the intercooler hose may reveal water dumping out. VW has many TSB's for this issue, but won't perform one unless you're having troubles. This is caused from condensation building in the EGR, then dribbling down to the intercooler. This can cause something as little as a stumble in idle or driving, or something as serious as catastrophic engine damage when it hydrolocks(depends on the amount of water). Many members report a spirited highway drive clears water out.
-Super easy to start in the cold and are very quiet, much more so than the BRM.
-DPF's do steal fuel economy and performance to lower emissions. Once removed, up to 10mpg increases are possible. DPF's can last up to 200k miles. Ash builds up when soot is burned off, and enough collects and can't be removed, therefore the DPF needs to be replaced. If you don't live in a CARB area, REMOVE IT! Your engine will thank you big time!
2015-Present(CR EA288 2.0L TDI) 150hp / 236 ft/lbs of torque
-This is the first year of AdBlue(Urea), refill intervals are every oil change(10k miles)
-Based on the outgoing EA189, there are minor differences such as lower emissions thanks to the AdBlue system and a dual loop EGR system, more power due to software tweaks, lower internal friction for better economy.
-This engine is better on fuel than the EA189, but the fuel savings are offset by the cost of the DEF.
-Too new to tell if the EA189's common problems carry over
That's pretty much the main differences and common faults. Some things are left out, but this is what to look out for. The 1.9 BRM TDI will be lower cost to run, is slightly better on fuel, and is more reliable than the 2.0L TDI's, but they are more of a hassle to start in the cold, much louder at idle, and much less power. They do feel lethargic at highway speeds to be honest. The 2.0L TDI's are fantastic engines and are very flexible, but do have expensive common problems.
It all comes down to this: Do you want slightly better mpg and less common problems, or do you want more power and more refinement?
I love both. My sister has a 2006 BRM with 330k miles. It's been awesome and she's owned it since new. She's replaced the EGR system and will be needing a cam soon. I have a 2013 Jetta TDI. I love the power and the refinement. My sister says she noticed a big difference in power, and fuel economy is almost the same as hers. If I were you, I'd buy a 2014 Jetta TDI. It's the most updated EA189 TDI and has IRS as well as other upgrades from previous Jettas, as well as it will have a longer warranty than the older cars, so if the HPFP fails, you'll be covered for a long time. It's definitely the best year for the EA189! Happy shopping!