I keep seeing on various radiant websites the claim that switching my home heating system from a gas furnace to electric radiant heat will lower my heating bills. How true is this? Of course my gas bill will go down, but the electric will go up - so won't it cost about the same?

It depends on a whole lot of factors, not the least of which is the price of electricity in your market. In most local markets time gas-fired ANYTHING of decent efficiency will beat resisitive electric of any type, radiant or baseboard- you may end up paying more.

Other factors include zoning and actual operating temps for each zone. If you have a wheezing 60% efficient gas fired air-blaster keeping the whole house at 72F and you instead zone each room separately with radiant-electric, keeping low-use or sleeping quarters 65F or less, and high use areas ~68-70F (which will FEEL about the same as forced-air at 72F) there's a good chance your operating costs will be lower with the radiant.

But bang-for-purchased-efficiency-buck you may get better results if you seal all duct joints with mastic (and test them to <10% leakage) , insulate the ducts in any unheated space (to R10 or better), and replace your old furnace with a condensing version before going to radiant-electric.

There is no simple answer- every situation is different, but electricity is rarely cheaper than natural gas (although it can be competitive with propane in many markets.)

I may be off-base on this but, by your question, do you mean to ask that if you switch the type of heat you have (forced hot air) to electric radiant, you will save money on your heating bill?! If that is the question, then the answer is no.

Radiant heating in any form may not necessarily cost less then what you already have but it will be more efficient if it is anything else but radiant. What is most important is how efficiently your home is utilizing the heat you generate as well as the net cost to switch.