Both can be equally accurate so you need to focus on other parameters like LR ballistics, recoil, and costs.
The 6BR is very well established and there are lots of equipment to load it. The 6.5X47L is sold on a much lower volume so things like dies are harder to get and when you do, bring $$$$
The 6BR has a case capacity that works very well with the common 105/107gr VLD bullets. Not super fast, but fast enough. Very low recoil. Excellent barrel life. It has been one of my favorite accuracy chamberings.
What you give up is BC. The larger cals offer a higher BC that will give you a tangible reduction in wind drift the further you go.
What you give up to use these larger cal bullets is increased recoil. Also, your shooting cost is slightly higher. Barrel life can also be shorter.
In the 6.5 family, the 6.5X47L is the smallest commonly used LR cartridge. The 6.5 BR is rarely if ever seen anymore. In my opinion, the Lapua is simply too small to get the job done with the heaviest 6.5 bullets. With the 120 to 130gr bullets, it does ok but runs out of steam with the 139 to 142's. I believe its design goal was to excell at 300m competition using 123gr bullets. To reduce wind drift vs the 6BR at this distance.
There is a difference but not much and you do have to put up with more recoil. Also, the bigger cal comes in handy when shooting for score. I would stick with an improved 6BR if I was in this type of comp.
So I consider it best to separate the two. The 6BR is one of the nicest 6mm's to use. A bit small but enough to get the job done for most shooters. Some who choose the 6mm for LR shooting are going to larger cases like the 6XC, 6 - 6.5X47L, improved 6BR's. Gives them more speed with the lighter bullets and nice velocity with the 115's.
I think we will start to see more interest in the 260Rem then in the 6.5X47L as shooters start to find they can't get the speed they want without the rig being really finicky and prone to pressure ailments. I expect to see a steady increase in interest in the improved 260Rs as well. Why there isn't an improved 260R wildcat with a 30deg shoulder sweeping the tactical and other mag fed shooting ranks is one of life's little mysteries (my Mystic uses a 40deg shoulder and not what I would suggest for mag feeding).
The 6.5 Lapua will do at elevated pressures what a 260R will do at standard pressures. Run the 260R to the same pressures and it will walk away from the Lapua. Same problem lies with the 6.5 Creedmore and this is bigger then the Lapua. Throw the Swede into the mix and it will walk away from all of these handily.
A faster 6.5 shooting 139 to 142gr VLD will offer a substantial reduction in wind drift vs the 6BR at LR.
You haven't given any indications about your other requirements so it is hard to say one is better then the other. Each chambering has its niche where it works well. Just have to decide if that niche suits your needs.
Jerry