As a medium RPer myself (in character around others ooc when in an area solo), I have often looked for the best possible RP where ever I play. I have played on 4 different servers now, the first two role play was nearly non-existant. About a year and a half ago I went to Landroval and have 2 75s and a couple of 60s there that RPed quite frequently, I found the RP on Landroval to be decent in most areas though what I did see around the Pony was not my style most of the time.
I left the game in december of 2011 for another game and played that game for over a year after many errors made by the company that operates it and the lack of quality RP and returned to LOTRO. My wife and I play together and she wanted to try another server, so we chose to give Laurelin a try. We've been back about a month now and I must say that their does indeed appear to be more "roaming" RP here than there was when I played on Landroval. To me it is exciting to see a group of people walking (even when on horseback) between Bree and the Lone Lands RPing as they go down the road, or even the other day when I rode my horse at break neck speed through thorins hall to get to the forges quickly before work and having someone "shake their head" at the recklessness at which I was riding.
So without making judgements against ones preferred styles or what constitutes what kind of RP, my suggestion would be to roll on both servers and see which fits your particular play style.
p.s. I play from Florida in the US during peak EST play times and I do see many people online on Laurelin.
To the OP I wish you the best of luck in your search and hope you find what you are looking for.
Eldest, that's what I am. Tom remembers the first raindrop and the first acorn he knew the dark under the stars when it was fearless, before the Dark Lord came from Outside.