Whatever you choose, do NOT go for EFU Site branch. Please, werna you will regret later. Plus ask the insurance guys in advance that you will repair your cars under insurance claims from your own mechanic, ad not give that to the workshops on panel.
By the way Adamjee and EFU both are swift in claiming processing. I have my car insured from EFU site, but they insist to go to their panel workshops which is not feasible for me, as I trust in my own mechanic for my car needs.