308 has been highly regarded by most I have spoken to with the ease you can find ammunition. But the people that like the 6.5 really love them.The comments from you guys is making me think 308.
Generally speaking, people always like the rifles they have, that's why they have them, and generally speaking, people tend to recommend the rifles (calibres) they have to other people. It's human nature.
The problem is, you're looking at shooting at opposite ends of the scale, Roe, to boar.
I don't have a 6.5x55, but I do have a 6.5x47, and it does a very good job on deer, but I wouldn't want to use it for boar, unless I was shooting from a high seat, at circa 50m-70m to a feed station. I also use a 7x64 for boar from a high seat, and even with this, I've had more runners than i'm happy with, and that's with a good heart lung shot.
A 308 will do everything, with a wide rand of bullet weights, up to 220g. If you were doing more boar hunting, especially driven, I'd be suggesting a 30-06.
I shoot a fair bit of driven boar