SlimBean has worked great for me on my S3. I can't say the same about SlimKat, as you can see in the thread I just created. Never tried any of the others. I'm hoping I can get my SlimKat fixed, and that it isn't an odd hardware fault.
@azotre: I'm late, sorry. My advice: Slim LP. As all LP-ROMs it fights against low S3-RAM, but if you keep your system slim, it runs stable&fast&charming. JB&KK are unsafe and MM-AOSP-builds are experimental until now.