As someone who loved 4 and was fairly ambivalent about 5 and didn't finish 6, I would say there's a lot of little things that made 4 better. Mechanically, the inventory system in 4 worked really well. Handling the inventory in 5 and 6 felt really cumbersome, especially the item trading. Resident Evil 4 had good level design. The environments felt better to fight in when playing RE4, and the lighting and general alien feel of the environment kept it from feeling familiar and comfortable. I felt like enemies had an easier time mobbing you, making for a more tense experience. Interaction with the shop keeper allowed for more variance in weapons and gunplay (as did the larger inventor space), and the ability to find pieces that could be combined into more valuable items rewarded exploration and being thorough. Most importantly, to me at least, was that the game still felt tense. Despite it being more of an action game, the lighting, enemies, and environments made the game still feel intense to play through. Kept you on edge. I never felt like I could go completely rambo, even late game when I probably could have (until the end, when it got all action set piece). In RE5 it was just a shooting gallery, and the co-op removed any sense of dread an encounter could have. When I did RE4, even when I had played the game before, I found myself gripping the controller and swearing at the TV as I ran around dealing with the enemies. In RE5 I felt no such thing, just casually plowing through enemies in an non threatening environment.
RE5 and 6 might have copied the action orient 4 introduced, but it lacked the same intensity, leading to bland experiences.