No, 3rd rail is not less expensive, mainly because for a given load, you need more feeder stations, to overcome the greater volt drop. There are something like 20 feeder stations on the south coast line between Brighton & Portsmouth, it's been estimated you could save the cost of renewing all but 2 of these by converting to 25kV OHL. Yes there would be a cost penalty in associated civils work to achieve clearances, but for a high intensity, high speed service, with power-hingry trains like IEP or Pendo, there is no real alternative to 25kV OHL. Not that I'm suggesting converting the south coast line should be converted, but I know it's been looked into.