The DualShock 4 does have pressure sensitive triggers, it just depends on what you're using it with since the triggers have both a digital input and an analogue axis input. When you're setting up your binds the game might prioritise the digital input.
DS4.png
The circles represent the digital button inputs in the language I use, the red ones are active. The U and R axis bars are for the right and left triggers respectively. I had the right held down halfway and the left entirely and those are the results. I have no idea if this is going over the top just to demonstrate my point but I thought it would be a nice example. Of course, by all means dislike the triggers if they don't work correctly in the games you use them for.
In response to the initial question, my favourite controller is the DualShock 4. But you probably guessed that already.