I can't speak for the two door JK, but I own both a 99 TJ and a 2009 JKU(four door)
I much prefer the sound of the TJ, but on long trips the JK is tons better.
A TJ is the classic WW2 Jeep taken to it the max. They are still pretty easy to work on and don't weigh much. Their primary advantage over past models is that they switched to coil springs instead of the old leaf springs.
The JK brought the wrangler into the modern era. There was a massive boost in complexity, with most functions being controlled by the central computer. Which is good in some ways. With JSCAN app and a blutooth dongle you can change a number of things about the jeep. Most notably the speedometer to wheel size ratio without having to change out a gear in the transfer case like you do in a TJ.
With that complexity comes the problem with all modern vehicles. How much can be done by the weekend DIYer. JKs are well known for the electrical gremlins that can pop up. There is not however anything inherently wrong with JKs. Many of unreliability issues are because they tend to stay on the roads far longer than other vehicles, along with people driving them in ways you wouldn't drive a normal car.
There are two primary versions of the JK.
2007 - 2011 use the 3.8 V6 engine with around 200 Horsepower. It is a good engine, but considered a bit underpowered if larger tires are wanted, especially if you get an auto transmission, as the 4 speed is not very well liked one. My 2009 rubicon has the 6 speed manual and because it is a rubicon I get a 4.10 gear ratio. This engine is however much easier to work on that the later one. I'm just about to roll over 200K.
2012- 2118 JKs have the 3.6 pentastar. This is a very good engine. The new JLs still use this engine. The horsepower was upped to 285, and a 5 speed auto gave the JK a good weight to power ratio. Making the manual transmission no longer the default better option. These years are going to cost quite a bit more as much as double the price of early JKs. 2012 was a somewhat buggy year, and to be somewhat avoided.
Both of these engines got used in many different vehicles, so getting parts is not a problem. Newer cars are always a bit more expensive to work on because of the complexity. Ride quality on JKs is a big leap up from TJs, though you do loose a bit of the toss around ability of the TJ, but on long drives the JK wins in all ways.
. JK is bigger and feels bigger than the old ones, not a bad thing but following a TJ on a tight twisty forest trail had me wanting one several times. OTOH, creature comforts 
