LR4 seems to have fewer transmission and differential issues, and except for the early ones, EAS seems to be better.
Gas mileage is marginally better on LR4 - extra load of horses allows it to stay in higher gear and lower engine RPM.
Overall, an LR4 is a better vehicle - with a lot of caveats, almost all of them engine-related.
Fuel system: fuel tank filter/flange leaking gas -> recall job, followed by impending low pressure fuel pump failure. I have not had high-pressure fuel pump failure yet, but apparently it does happen. Low pressure fuel pump controller also can fail, but it's a $100 part that can be replaced on the side of the road if you have it along.
Timing chain tensioners seem to affect not just early LR4s but all years. If you're buying an LR4 and this has not been done, factor in 5-7k in upcoming costs. Plastic crossover coolant pipes seem to have about 100kmi lifespan - if those haven't been replaced after 100k, you're on the borrowed time.
I am sure that's not all there is.
I have owned three LR3s, one with a HD package, and two LR4s, again one with the HD package. I agree with all this.
The LR4 was an evolution of the LR3 and I can't think of one area it doesn't noticeably improve on the LR3. The interior is far nicer, and it feels much more contemporary. They both look like fridges, but the LEDs, painted large flares, and newer door handles keep the LR4 in the modern era. I always found the LR3 to be adequately powered like a stock 4.6 D2. The 5.0 on the other hand is really fun to drive. It makes you forget how heavy the truck is, though you do still feel it when stopping. My 13 LR4 is noisy but not as noisy as the totalled 11 it replaced with the same mileage. It also sounds about the same as my friend's 20 L405 SC. So, I think there is some truth to the updated chains in 13s. They'll probably all need chains done if early owners followed the 10K mileage interval. I remember my LR3s getting about the same city gas mileage my 4.6 D2s did, with somewhat better highway numbers. My LR4 does much better on the highway, around 20-21mpg with heavy mods. Around town it's 15 or so.
Brakes on both are good. I don't like the V6 headlights or swoopy mirrors, but I don't like the V6 engine and knob shifter anyway. Too bad they never paired the V8 and 8 speed. The V6 is pretty much the same problem child with less power and its not as smooth. I think the LR4 handles sportier driving better, but it has been a minute since I owned a LR3. The LR4 paint seems to be higher quality, but it could just be that LR4s are newer.
It all boils down to what you value most and what your budget allows. If reliability is paramount, a LR3 with updated suspension components is great. It's certainly more modern and liveable than the Discovery 2 it replaced. When shopping high mileage cheap trucks, I'd chose the LR3. If you want a really nice modern LR that is fun to own, but may bite your wallet, the LR4 is tough to beat.