Do you mean actual appliance brands and models, or retailers?
If the latter, we recently got quite a few items from Dalzells in Markethill (Co. Armagh). For the package of appliances we'd put together, they came in 15-20% below any of Powercity, Harvey Norman or DID. We checked that they were charging VAT correctly, and that all warranties and service agreements would apply in the Republic, and everything was fine. They deliver free to Dublin, but I don't know about the rest of the Republic. I normally prefer to use local retailers where possible, but the price difference was just too substantial to justify it.
Standard disclaimer - satisfied customer only, no other connection.