Well, the rules say that a double-based element only gains a +1 when in close combat with foot in Good Going (see “Rear Support” on page 11), and that the first double-element lost counts a two (see “Winning And Losing The Battle” at the bottom of page 12).
As Stevie says, those are the main benefits in the rules, of course if you also have some solid Blades and put them next to your 8Bw they'll get support for that in combat against foot as well, so your 8Bw can be on a +4 against foot in close combat, which should help them survive a bit longer.
Of course in shooting none of that matters, (weird when they have a row of spearmen with shields in front, but there you go) so maybe not a good idea to get into a firefight with 8Bw v 4Bw as your first 8Bw loss counts as two elements.
Just to clarify, the rules say you should have 8 models per base for an 8Bw, rather than the 12 or 10 shown in the pictures, but I can't imagine anyone objecting to those shown, but to clarify, you don't have to provide more than 8 models per base.
Eagle6, welcome to the DBA life. Much fun and discussion. Please consider the point made by Paul in his first comment. It reminds me of what a leading figure in the wargame life once wrote: “ Historical gamers see an elevated area as a tactical advantage but Ancient gamers see it as a +1. “ Perhaps the question to ask, is not what is the advantage of 4Bw over 8Bw but what looks better or which is historical, including in the army list. Phil writes, "Victory as well as realism under these rules is mos tlikely to be achieved by thinking of elements as bodies of real troops rather than playing pieces, and using them historically. "