I have owned a Liteon 20A1P for about 25 days days, and a Pioneer 111D (very similiar to the 112) for 10 days....
One very important fact:
The LiteON is a far superior Scanner, so if your big on scanning get a LiteON and read no further. Its also a great burner, you'll love the drive.
However, if the scanning isn't so important to you, heres my observations so far:
The Pioneer burns more consistently than the LiteON. I've had some magnificent burns with my Liteon, see here and especially here - Those burns are gorgeous - I am yet to get a burn on my Pioneer with only 9 total PIF errors and probably never will. My first 1 Pioneer burn scans are available here and here - These are also great scans. I've done about a dozen burns since then and they look about like this, consistently very very good.
The thing is that the Pioneer burns have been very good burns, although never as perfect as those 2 LiteON burns above. However, the majority of my LiteON burns haven't been as good as the two linked above. They have been good, but not as good as my average Pioneer burn.
One new observation is that with junk media (namely the new Verbatim DVD+R MCC004 discs with PAP6 serial numbers detailed here) my LiteON Drive usually fails before the end of the burn reporting bad media. My Pioneer completes, the scans usually aren't good (250,000 total PIE's and maybe 4,000 PIFS with spikes up to 10) but the drive is able to burn the entire disc. Not sure if this matters or not - If the media is trash, I personally dont care if the burn completes because I'm just going to reburn - but it might be a sign that the Pioneer has more more robust burning capabilities than the LiteON
So I guess what I am trying to say is that if you want consistent high quality burning (lets say ranked at a 9/10) I'd say get a Pioneer. If you want consistent good quality burning (lets say ranked at 8/10) with an occasional perfect rock star 10/10 burn, get a LiteON.
Either one will be a good choice if you stick with high quality media. Or you could always get one of each like me, I am going to do the majority of my burning with the Pioneer and always use the LiteON for scanning.