What are the pros and cons of delta re-hedging an option combination (straddle, strangle etc...) with options of the same underlying rather than with the underlying itself? I am having a hard time finding litterature on the subject.
Delta hedging with other options would give you exposure to the implied vol dynamics of those options. Delta hedging with the underlying gives you exposure to the realized volatility of the underlying.
It will also change the gamma/vega of your position which can be a significant improvement over just hedging with the underlying.
On top of my head, there are two reasons. One is that the underlying may not be accessible, while you can buy/sell options on exchange or OTC. The other (more important) reason is your position on other greeks (gamma, vega, etc). With appropriate options you can adjust both your delta and other greeks.