Well, I've played with it a lot. Actually, "them" as I have 3.
Even on their website they say:
What is the accuracy of the RG-11 Rain Gauge?
The Hydreon Rain Gauge is not as accurate as a properly maintained Tipping Bucket in ideal conditions.
We do not claim an accuracy specification for the RG-11 Rain Gauge. The RG-11 is very repeatable, and over a variety of conditions will yield an average result that is reasonably close to that of a tipping bucket. But, for any given rainstorm the result can be off by as much as 2:1 in either direction. Even this is not an upper limit.
The strength of the RG-11 is that it works in many situations where a tipping bucket simply does not. That is, the Rain Sensor is vastly more accurate than a tipping bucket that has ceased to work properly due to dirt or mineral deposit or mechanical difficulty, or a tipping bucket in a mobile application that is constantly giving false indications due to motion. The RG-11 is more accurate for a small (but in some applications, meaningful) amount of rain, such as 0.01", that will simply not register in a tipping bucket.
This said, if you do not need the ruggedness of the Hydreon Rain Gauge, and maintaining the tipping bucket is not a problem, use a tipping bucket.
That pretty much sums it up. You might try contacting them and seeing if the firmware has been improved since it was introduced. And, at $60US it's inexpensive enough IMO to buy one to experiment with.
As you note, I don't know what you would gain from using a funnel. Like any rain gauge, it's apparently designed for the area of the clear lens. I say "apparently" because I did talk with them once and they either didn't know or wouldn't tell me the active diameter or area.
I'm using them more as an "It's raining" indicator, and also as a faster intensity indicator than a tipping bucket.