Chromalux Electric Boiler Replacement for Radiator System
The answer depends on where you are, what your local energy prices look like,  whether you already have gas coming into the house, whether you're going to be there long enough for investment in a new system to justify its cost...

In my area, gas and oil have historically alternated as most cost-effective, with electric heat always being most expensive. 

When I bought it, my house had a 1945 oil boiler, inefficient by modern standards and with a slightly leaky tank as well. I budgeted for replacing it when negotiating the purchase. I personally prefer gas and already had gas coming into the house, so that's what I chose -- a direct-vented high-efficiency gas boiler, with new pumps, feeding the existing radiators. 

(Actually,  I was very interested in the small gas-fired cogeneration plants starting to be sold as heating systems ... use the gas to run an engine which runs a generator, sell the electricity to the grid and use the "waste" heat to heat the house -- but for good or ill, they were only available for forced-hot-air systems and I wasn't ready to replace everything or deal with having only one or two trained technicians in the entire state to maintain the thing. So I'm just selling solar to the grid.)

One thing to keep in mind when upgrading a heating system:  Old units drew combustion air from their surroundings, drawing (cold, in winter) replacement air into the house. New units are direct vented, meaning they draw combustion air directly from outside, so you don't lose as much heat out the exhaust.  But their greater efficiency also means less heat lost to their surroundings, so the basement may actually become cooler rather than warmer unless you remove some pipe wrap to get more heat into that space... or add a zone and radiator(s) for the basement.