I also have argued with both. But my results have been quite different. I have found both to be pretty much equal in their treatment of libertarian ideas. The problem you seem to have experienced, is one of language.
The liberals do not speak the same language as conservatives do. They don't set the same priorities that conservatives do. They do not fear the same compromises which may occur from untimely advancement of particular issues that conservatives do. Learn the language and value system first, and you'll find liberals are as open as conservatives to the libertarian philosophy.
I assure you, that should a liberal libertarian, completely unaware of conservative values and language come on to Free Republic, and start spouting off using liberal oriented rhetoric and values, that libertarian will receive just as much insult, threat, and disrespect as you have received from liberals. And rightly so.
As a matter of fact, I've seen two different liberal libertarians, at two different times, get a well deserved royal trouncing here at FR. Even the libertarians here didn't recognize them, and assumed they were advocating what in fact they weren't advocating in the slightest. I think in both those cases they didn't try to get past the misunderstanding, as they saw the alternative understanding as no better.
I regularly talk about peoples right to keep and bear arms with liberals, even those who oppose such rights. Usually it ends with them saying that I have a lot of good points. I know I have convinced a number of them on that issue (well maybe not me alone). I have never heard a wish of harm to me or mine, do to that stand.
I've criticized Reagan policies to conservatives but I've never been called a 'Reagan-hater'; but it's impossible to discuss any Cl*nt*n scandal with a leftie without being called a Cl*nt*n-hater.
The problem with liberals as far as being open to the conservative philosophy (that part this is shared by both republicans and libertarians) is this :
Liberals have a hard time wrapping their mind around personal responsibility. They don't place blame for problems where it lies. Even when forced to place blame where it lies, they still have a hard time with it.
Whether it's placing blame on the criminal (rather than on the gun as they are so quick to do), or saying one murder is worse than another based on the skin color of the victim, they try to dodge personal responsibility.