For as far as i know about the fallout universe the pre-war era was marked by an unprecendented energycrisis due to oil-stocks running out dramatically, which forced nations around the globe into inventing alternative energysources. The first and only nation to succed in this were the United States, who made nuclear fusion possible for commercial use. This however was a slow and costly proces, which only fully developed in and around the Washington D.C. area. As a result it was one of the very few areas in the country to have a fully nuclear powered ecnomy before the war. The war continued simply because oil was still a tremendously important product, evermore because China, the instigator of the war, was completely dependent of it. Furthermore there was also an ideological struggle between the two contries respectively between communism and capitalism. The United States Government was as well completely corrupted by the Enclave and did no longer strive for a solution of the problem by conventional war but rather by a massive cleansing that would wipe out communism, in the form of a nuclear holocaust. Which is exactly what occured just several years after nuclear fusion was introduced into society.
In a nutshell Fallout's world was the future predicted in 50's combined with bit more human fallability than 50's predictions had, then it was nuked.
If the the Nuclear Holocaust caused more damage than a normal one would, because of the nuclear fusion technology used in various products is questionable. First of all, this technology wasn't very widespread but if we narrow the question down merely to D.C. it remains interesting. Still, i don't really know, it simply depends on the way physics work in the Fallout Universe. Radioation in the Fallout Universe for example, causes monstrous mutations whereas in our universe it merely kills almost every kind of DNA-based life.
Also if one were to shoot at a nuclear reactor core in our universe nothing would happen simply because of the lead surrounding the reactor, but in the the Fallout Universe cars explode after a few well-placed shots. The most accurate conclusion i can make is that it would in fact cause more damage, since the nuclear bombs in the fallout universe were of a relatively low-kiloton range wherein any surrounding combustable or explosive material would make a difference in damage proportion, in comparison to our nuclear arsenal from the cold war, which mainly consisted of higher kiloton and even megaton nuclear warheads that would simply oblitare and completely destroy everything in their way.
Yield of weapons in real life is kinda two fold, there is relatively big warheads and very small ones. When it comes to numbers, in US and Russian arsenals there were tens of thousands of low yield tactical nuclear weapons, bigger strategic warheads peaked in about bit over 12 000 warheads per side in mid-80's. Megaton class warheads were eliminated from arsenals mostly before mid-80's, probably only really huge warhead still in service is one carried by SS-18 mod 3 (that is NATO designation of system, Russian designation is R-36MUTTh), it's yield is around 25 megatons. Few of those might still be in service, but unfortunately those are quite high list of weapons due to be replaced with Topol-M. It's sad to see that most powerful weapon system retired, R-36 rocket family was pretty awesome in it's capability, there was Fractional Orbital Bombardment version that could have used with across south pole trajectory, it could have been utilized with much less warning time as USA didn't have that complete radar network in south as it had in north. Real multiple warhead MIRV versions had 8 or 10 550 to 750kt warheads, there was another canceled variant that could have had up to 40 250kt warheads. Single missile that could destroy an country quite completely, it was canceled due to treaties that limited amounts of total warheads, it was strategically more sensible to build missiles with fewer warheads due to greater survivability in case of sneak attack.
Effects of nuclear weapons impact is not that well studied subject, it was studied a lot, but findings were often contradictionary. Houses were built on nuclear test sites, as were factories and even forests were set up in deserts. Still neither Soviets or US built a real town to blow up, due to costs. Fallout patterns after tests conducted in atmosphere varied a lot. Seemingly small details in weather might change outcome of nuclear strike a lot. Think about how much rain can absorb energy from nuclear detonations heat wave or how much of that same infrared spike gets reflected from snow cover. Totally flattened pictures from Hiroshima and Nagasaki also have few reasons why they aren't whole truth due to local conditions. Nagasaki was in valley and it made few parts of city to be hit by reflected pressure wave multiple times. Lot of buildings were constructed from wood, really huge part when it comes comparing with western cities and their architecture.
True effects of nuclear war would be horrible and reality is often more absurd than fiction. In 1983 when plenty of things were going off around world and risk of nuclear confrontation between east and west was at it's all time high. President Reagan studied actual estimations of effects of nuclear war only after three years of assuming office. Single Integrated Operational Plan was US basic nuclear warfare playbook, it included estimates on casualties in multiple different scenarios. Brutal reality in nuclear warfare is actually really brutal, US estimate for own civilian casualties in war with Soviets was about 150 million. Ironical is that it is the best case scenario, every thing in war goes as planned for Americans. Peachy, ain't it. One of funniest cold war damage estimations is what would happen to Boston in case of hit with 20 megaton warhead from early 60's, it hilarious when it comes to needed medical capability, each doctor would have had thousands of patients needing surgery in hours. Think about it, every surgeon would have to perform possibly thousands of surgical operations, each of those surgical operations could take hours and patients would be needing those possibly bit earlier than they are going to get it. Stuff is pretty close to division by zero.
Mutations do occur due to radiation, they just aren't extra limbs or scaled skin, those are more like downs syndrome or missing limb. Well, cancer is really most common mutation.
Yeah cars....
Highwayman from Fallout 2 had pretty similar looks with 1957-1959 Chrysler 300's, it probably explains lot about name of fictional one's manufacturer.