I don't know where to start reading the Punisher. Remender's run?
They're completely unrelated, Rucka's run and Remender's. Remender started his tenure during the whole "Norman Osborn takes over everything" phase of Marvel and positions Punisher as one lone man fighting the takeover; then, things go to crazytown with the so-absurd-it's-amazing Frankencastle saga. It's atypical Punisher stuff, and very enjoyable, but it eventually had to end and Remender puts all the toys back in the box in the finale. Rucka follows with a more grounded, procedural drama approach to the material, refocusing the Punisher on his war against organized crime in New York City as filtered through the Marvel U. He keeps the lead character very enigmatic, and builds up a strong supporting cast around him to fill up the world they live in. Which worked extremely well for me; Rucka's tendency to not focus solely on the lead, to give equal time to characters like Rachel Cole-Alves and Walter Bolt, is one of the things I love about his writing.
People will say Ennis, but apart from the very early stuff like "Welcome Back Frank" and "Born" I've never really cared for it. But I know that's a minority opinion.