that controlling the game without pressure-sensitive buttons makes the controls even worse
In-case anyone here is wondering, pressure-sensitivity works in PCSX2, if you use SCP Server, there are two files located in the Bin/Win32 folder, a custom LilyPad.dll and XInput1_3.dll. Place the Lilypad.dll into the plugins folder of PCSX2 and the XInput.dll into the root of PCSX2 (Where the .exe is located). Change the pad plugin for the customized one, and you should be able to tick native DS3 mode.
For other controllers, I'm not entirely sure. I've seen threads at PCSX2 where some PS2 adapters support pressure sensitivity, but can be iffy with Lilypad, and for the Xbox 360 controller, I don't know if that supports pressure sensitivity in the first place.