It's a few years since I contracted, but normally the agency does not give you an option - they require an opt-out as condition of awarding the contract. If they're offering you the choice and you're going through a brolly, then opt in.
For the NI_Er: strictly speaking, *you* don't pay it, your employer does. Which in your case is the brolly. In the case of a Ltd Company contractor, your own company pays the NI_Er. *Someone* has to pay it, and from your point of view it's coming out of the headline (gross) contract rate.