One way of looking at it is to use case capacity with 6BR as the base, its capacity treated as 100.
What you get is (approximately):
6BR ................... 100
6 Dasher ........... 110
6/22-250 ........... 114
6/250 Sav ......... 116
6mm SM ............ 119
6X47 Lap .......... 126
6XC .................. 128
.243W/WSSM ... 140
The rule of thumb is to divide the % change in case capacity by 4 and your get the likely % change in MV, all other things being equal (bullet weight, barrel length and chamber throating, and particularly the peak chamber pressure that the cartridge and loading generate.)
So, you expect 6X47 Lapua to produce a 26 divided by percentage MV increase over 6BR, ie somewhere between a 6 and 7% increase, but at the cost of considerably larger powder charge in % terms and a considerably reduced barrel accuracy life in terms of round count.
Taking 6BR as the base again and working on 2,800 fps MV for a 100-107gn bullet, the MV improvements from the larger cartridges are around:
6 Dasher ................... 70 fps
6/22-250 / 250 Sav . 105
6mm Swiss Match ..... 140
6X47 Lapua .............. 180
6XC .......................... 200
243 Win / WSSM ...... 280
You can see you've basically got four groups - the 6BR itself; the improved BRs + 22-250 & Savage wildcats; the 6X47 Lapua + 6XC; .243 Win sized cartridges.
The Dasher and 6BRX have a superb reputation for performance and I don't see why the only slightly larger capacity 22-250 / Savage wildcats would be any different. (But who knows until you try!) If you want top-notch brass, you've got it with 6BR and its variants and the .22-250 wildcat, don't know about the Savage.
Go above the capacity of the two smaller groups and you start to pay a price in terms of barrel life and also start to have less flexible cartridges in terms of powders you can use and the ease of getting loads sorted that work really well. I'd personally stick with the BR and the next capacity step up (and that's despite my having a very nice 6XC as a mid to long-range BR and F-Class rifle). When you get to this size of case my own inclination if starting with the 6.5X47L case would be to leave it at 6.5mm - another very fine performer, very flexible in what you can use it for, and one that gives good barrel life when weighed against the ballistics.
As others keep saying, it's hard to beat the basic BR and if you go for a 1-8" twist barrel and 'BR Norma' throat, my experience with the cartridge says that configuration can still produce amazing results with the 55gn varmint bullets even when they're making an almighty jump - so a good BR copes with anything between 55 and 107gn. If you must shoot 115s, pick one of the bigger cartridges, but I've found with the XC that they don't somehow live up to their promise even in long-range F, and others I've spoken to have come to the same opinion with the mid size sixes, although I know they do have their following.
The other thing you don't mention, and nobody has picked up on that I've noticed, is whether you want the rifle to be a repeater or not. If magazine feed is important, the BR and improved BRs are not entirely, but virtually ruled out, while everything else feeds fine.
I hope putting it this way helps with your choice a little. They are all, or certainly should be, fine performers, and it's down to what takes your fancy at the end of the day, maybe other factors like how easily / quickly you can get a chamber reamer and brass. Have fun anyway!
??? Let's change calibers a second. Interested in the pro's and cons of the 6CM and the 6x47. Can anyone give me a comparison, pro's and con's? Keep in mind I want to shoot the heavies to include the 115's. Best twist rate and barrel length. Use again would be varmint, target, F-open.
? I'm sorry, I couldn't help myslef 
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