Of the top of my head I had an Ogre and a Raven that served me very well. If the explosive rounds in BL2 were like that of the Ogre (same velocity as normal rounds with instant explosion) then I'd probably just use an explosive AR in BL2 but unfortunately that is not the case. I'll try to start BL1 up later and look at my specific AR stats.
Have you tried using the explosive Assault Rifles against targets that don't move much? I find their damage to be great against armored targets like Nomads (shielded especially), Goliaths or Badass Varkid. I still use it against smaller bandits, but they jump around
a lot, which makes it significantly harder. Sometimes, I treat the AR a lot like my Double Anarchy in Borderlands 1, which probably isn't a good idea (it works though ). The AR takes awhile to spool up, and doesn't reload nearly as fast as the Anarchy gun did.
I actually need to find a new Sniper Rifle. I have a DAHL one that fires in burst while zoomed in (i.e. almost all the time). It doesn't matter in most cases, but it's terrible in arena fights. I simply waste too much ammo, and I'm way too restricted to be able to easily get more. However, that SR can be
deadly against those stupid Crystalisks. Those things can really deal a lot of damage, but are taken down fast by sniper bullets to their legs.