There is no doubt in my mind the 5.56 makes the most sense for a training, 3 gun, varmint  or a HD round, they feed with no issues, everyone makes mags and every part is cheap. There is just no need to look for any other caliber when considering the uses above. 
The 6.8 has a dual use as well, it can be a very effective legal  hunting cartridge and a HD round also. The terminal performance on game is much better than most other cartridges, making it the best choice for deer and hogs.  Several Goverenment agencies have moved to the 6.8 because it offers 80% of the power of a 308 on a much lighter platform. It is the second most popular AR15 cartridge in terms of sales and suppliers.

 

Nitro/ QPQ barrel treatment corrosion comparison during a salt spray test.
chrome and nickel had at least 4 times the area of the nitro barrels corroded.

This is a stainless barrel that has been Melonite treated. the right end was bead blasted then the barrel was placed on a wet paper towel
covered in table salt, wrapped up in another wet hand towel and kept wet for 1 week. That was in 2009, this is how the barrel looks in Feb 2012
It has been wrapped up in the salt for over 2 years. Only the area where the melonite treatment was blasted off did it show any corrosion.

Corrosive ammo or primers are made from Sodium perchlorate not sodium chloride(common table salt). These melonite barrels are very resistant to
water and salt water but not corrosive ammo. After shooting corrosive ammo you must clean the barrels the same day or pitting will occur in the bore.

 

Nice bullet line up, thanks JerBear

Barrel comparison chart by Paulo Santos

 

6.5 Grendel using Bill Alexanders max loads in a 16" barrel- zeroed at 200yds drops at 300yds.
Due to velocity dropping below the expansion threshold 300 yds is about max for taking deer or hogs with either caliber.
The same temp, pressure, line of sight and program used to figure all drops in both calibers.
100 Nosler-2600fps--drop 9.4/801 ft lbs
107 SMK-2545fps-----drop9.5/878ft lbs
123 SMK-2472fps----drop 9.4/1083ft lbs
120TSX-2472fps----drop9.8/984ft lbs

6.8 SPC SSA factory ammo 16" barrel
100 Nosler-2700fps--drop9.0/809ft lbs
110 Nosler-2630fps--drop9.0/939ft lbs
110TSX-2630fps---drop 9.5/856ft lbs ------added
6.8 handloads max
100 Nosler 2950fps---drop 7.4/993ftlbs
110 Nosler 2750fps--drop8.2/1040ftlbs

Both are very close for hunting out to 300yds.
The 6.8 loses apx 80-100fps dropping from a 20" barrel to a 16" barrel.

6.5BR- 16" barrel
100TTSX -2900fps --drop 7.4/1040ftlbs
120 TSX- 2700fps-- drop 8.1/1211ftlbs
120 Nosler-2700fps--drop 8.0/1233ftlbs
123SMK-2700fps--drop 7.8/1327ftlbs

Available factory ammo

6.5 Grendel
Hornady-123 Amax
Wolf -120fmj
-------123 soft point
AA----120 Nosler
-------123 Lapua
-------129 SST
-------90gr TNT

6.8 SPC
BVAC-------110 Vmax
---------------115OTM
Corbon------110 TTSX
--------------115 SMK
--------------115 subsonic
DoubleTap--95TTSX
---------------110 Vmax
---------------115 FMJ
---------------110TTSX
---------------110 OTM
Hornady-----110 Vmax
---------------110 OTM
---------------120 SST
Hunting Shack-110 Vmax
---------------115 OTM
Rem.---------115 FMJ
---------------115 HPBT
--------------115 corelokt
--------------115SMK
Sellier&Bellot-110 TTSX
-----------------110 Vmax
SSA------------85 TSX------------SSAs loads available in Commercial and Tactical velocities
----------------95 frangable
----------------97 AP
----------------100 Nosler Accubond
----------------110 Nosler Accubond
----------------110 Sierra Pro hunter
----------------110 TTSX
----------------115 SMK
-------------95gr Barnes TTSX coming soon

Suggested reloading components

Hornady small primer brass for the best accuracy, it is more consistant in weight and neck thickness.
CCI -#41 and 450 small primers, Wolf small magnum primers for a less expensive option(apx $18/1000 from Wideners)
H322 powder for the best accuracy, 29.5 is max case capacity without compressing the load. 
RE 10X for 100-115gr bullets where more velocity is wanted- 29-29.5 gr but work up to it.
RE 7 for 85-95gr bullets- 29.2 gr is standard but work up to it.
H335 is a good all-around ball powder for good velocities over a wide weight range of bullets.
AA2200 a new powder on the market , many shooters having good luck with it.
Sierra 110gr Prohunter bullet for great accuracy and terminal performance on deer
Barnes 85, 95 and 110 TSX  for the best terminal performance on hogs
Speer 90gr TNT for great accuracy and peformance on varmints and yotes.