Yeah thanks guys, you can both have some internet points! 
The risk of checking behind is bad cards coming on the turn and allowing his x/f range to improve. Obviously there are more bad cards for 78s than A8s. The risk of betting the weaker hand is it gets less value or value towns itself sometimes and beats less hands in villains range.
Comparing the two
- I gave BB two ranges, a wide range (WR) and a tighter range (TR). Because both kinds of ranges are fairly common and thought it would be interesting to see if they differ too much.
How do the hands do against BB's entire range that sees the flop?
A8s is the best hand 78% (65% equity) of the time against BB's TR entire range that sees the flop.
78s is the best hand 71% (59% equity) of the time against BB's TR entire range that sees the flop.
A8s is the best hand 82% (67% equity) of the time against BB's WR entire range that sees the flop.
78s is the best hand 75% (61% equity) of the time against BB's WR entire range that sees the flop.
How do the hands do against BB's x/f range?
BB TR
A8s against BB TR x/f range has 82.3% equity
78s against BB TR x/r range has 80.4% equity
BB WR
A8s against BB WR x/f range has 84.6% equity
7s8s against BB WR x/f range has 82.6% equity
How do the hands do against BB's x/c range?
A8s is the best hand 65% (51.7% equity) of the time against BB's TR x/c range.
78s is the best hand 51% (44.3% equity) of the time against BB's TR x/c range.
A8s is the best hand 68% (52% equity) of the time against BB's WR x/c range.
78s is the best hand 48% (40% equity) of the time against BB's WR x/c range.
From this I think we can take away.
- There is a pretty decent difference in the value we get against villain's x/c range from between betting A8s and 78s. Between 25%-40% depending on how wide BB is calling.
- The vulnerability of x/c hands against villain's x/f range isn't really that bad. With the difference between A8s and 78s only ~2%.
So I think this shows a good argument that A8 is the better bet.
I also did 22.
How does 22 do against BB's entire range that sees the flop?
22 is the best hand 54.3% (37.5% equity) of the time against BB's TR entire range that sees the flop.
22 is the best hand 57.6% (40% equity) of the time against BB's WR entire range that sees the flop.
How does 22 do against BB's x/f range?
BB TR
22 against BB TR x/f range has 56.1% equity, best hand 77%
22 against BB WR x/f range has 58.4% equity, best hand 80.7%
How does 22 do against BB's x/c range?
22 is the best hand 37.2% (26.5% equity) of the time against BB's TR x/c range.
22 is the best hand 35% (23.7% equity) of the time against BB's WR x/c range.
So I think with 22 an argument can be made for betting (for a bluff/protection/value or whatever u want to call it), because it's equity is so vulnerable to villains x/f range.