Operating costs would be similar, but establishing a new business unit would allow a slimmer organisational structure in comparison to the original group. Staffing costs could be lower as employment packages would be less than the existing VA packages. 'New' airline, 'new' EBA for the pilots. Hopefully they'd set up the new business properly and not use smoke and mirrors like QF/JQ do.
Offer absolutely no frills, therefore lowering costs yet again. Fly only one type again (say, the 737-NG) in the new LCC, therefore maintenance, training etc costs would be reduced. Overall, Virgin Australia does not have the lowest cost base, hence their move away from the middle ground and towards a differentiation strategy.
I hope they don't go down this path because of the reasons given in the first post. Secondly, lowering conditions affects everyone in the industry and personally I'm sick of seeing this happen.