As an owner of both drives, I'd opt for the 20A1H if you consider ODD usage a hobby of yours at all. The H42N/L, while a solid burner, isn't as fun to mess around with. The 20A1P/H has SmartBurn, OverSpeed, HyperTuning, and Online HyperTuning along with accurate disc quality scanning, better error correction, and faster ripping. LiteOn is also very good about updating their firmwares whereas LG is piss poor in this department. Codeguys is also kind enough to patch our LiteOn firmwares for FastBurn (higher RPM) and Enhanced OverSpeed.
Oh yeah, the LG support page will nauseate you too.
While the 20A1P/H may not be the best writer, it burns very well. Check out the disc quality scans in the LiteOn forum; dependent upon the MID and HyperTuning settings, a lot are even better than the H42N.