This won't be an argument for why Captain Picard is better than Captain Kirk (and anyway, why choose?). This will instead be a post about why we should be looking towards new nuclear technologies and winding down the old. We have a bad habit of decrying the problems of power plants built 40 years ago, and projecting those problems onto new plants.
There is some merit to this tactic in the case of the various flavors of Light Water Reactors that may be built in the future, as they are simply safer versions of old reactors. However, there are other technologies out there that have higher inherent safety than a LWR.
There are, in my opinion, a few major contenders for technology: Liquid Fluoride-Thorium Reactors (LFTR, pronounced 'lifter', a type of Molten Salt Reactor), and flavors of Pebble Bed Reactors.
Molten salt reactors were actually designed in the 60s, before the advent of the intercontinental ballistic missile. The US Air Force wanted a bomber that could fly indefinitely, and turned to nuclear power for an energy source. The MSR reactor design was the end product of that process, though it never reached a point where it was small enough to be put in a plane. Unfortunately, this design was axed by the Departments of Defense and Energy, as its fuel cycle typically cannot be used to produce material for use in nuclear weapons (something that was very important at the time). What was once a shortcoming is now an advantage.
The liquid fluoride salt thorium reactor is an MSR that is used to breed fuel, in this case converting thorium, a relatively abundant element, into the rarer Uranium 233, which is fertile for fission. This means that once the reactor is running (started perhaps, with material from decommissioned warheads, or from the stockpile of 233 the US governement is currently sitting on), it can run indefinitely, without additional uranium mining.
The liquid salt fuel is also passively safe, as it expands when heated, and expansion reduces the efficiency of fission. Reactor designs have been suggested where the reactor vessel bottom is a plug of actively cooled fuel salts; if there is a power failure, the plug will melt, draining the reactor into a storage pit, where the salt will cease undergoing fission, and cool into a solid block. Molten Salt Reactors also provide the opportunity to continuously process the fuel, removing valuable isotopes and fission poisons, allowing the fuel to be used up completely (as opposed to the very small percentage of Uranium used up in a modern fuel rod, which is usually less than 10%).
Pebble bed reactors make use of exceptionally durable fuel pellets to greatly simplify reactor design and improve safety. The carbon and ceramic 'pebbles' (about the size of a tennis ball) are much more difficult to melt than a modern fuel rod, fully contain the fuel, and can be cooled with gas, as opposed to water, and do not need control rods, instead being moderated by temperature. As temperature increases, power output (i.e. the rate of fission) decreases, and the system can be designed to passively shed heat in a cooling system failure. PBRs can also theoretically make use of mixed fuel designs, breeding thorium or un-enriched uranium into fissile material in the reactor, lowering fuel production costs, and increasing the technology lifespan (there is, after all, a limited amount of fissile uranium available on Earth, and it is costly to do enrichment). There is some question, however, about the flammability of the graphite fuel pellets. This design also calls for more mechanically intensive, destructive reprocessing (the 'spent' fuel pellets must be ground up to remove fission poisons, the reusable materials extracted, and re-manufactured into new pebbles). However, the fact that pebbles are constantly being cycled in and out of the reactor means that a more or less continuous reprocessing stream can be maintained.
I tend to come down on the side of LFTR type MSRs, as they seem to have a great many advantages over other designs. It's worth noting that all next generation nuclear power designs have significant technological and engineering hurdles to overcome before they could be put into production. I think those hurdles aren't so high that we couldn't do it in the near future, however, if we put our minds and wallets into the effort.
You can read more about LFTR technology (and nuclear power generally) at: http://energyfromthorium.com/