The kinds of reactors used in submarines and rockets, are known to have highly enriched uranium ~80% and CO2 as the moderator in subs, and carbon(graphite) I guess in rockets. What are the extra problems that arise compared to regular reactors? How are the control mechanisms more or less complicated?
Quick note: We don't use reactors in rockets. Instead, we use RTGs - chunks of radioactive material hooked up to a thermoelectric couple - to generate electricity from the natural decay heat. Typically we use Pu-238 because it has the best combination of decay heat, half life, and density. This is handy for space probes travelling past the orbit of Jupiter for electricity production, and it is also useful for Martian rovers which have to deal with the occasional dust storm. There were a few tests done in the 1960s regarding nuclear powered rockets, but we never implemented them for a variety of reasons.
To your main question - a big issue is security. If highly enriched Uranium falls into the hands of terrorists, that material can easily be used to make a crude fission bomb - the Hiroshima bomb essentially fired a Uranium shell into a Uranium target, briefly achieving critical mass and instigating a fission explosion. It's an unlikely scenario, but a risk that most governments have elected not to take. Military vessels are the exception, because have fun trying to take on a Nimitz class carrier.
The other problem is that highly enriched Uranium isn't necessary for most reactor applications. Nuclear reaction rates are equal to $\rho$ * $\phi$ * $\sigma$, where $\rho$ is atomic density (atoms/cm^3), $\phi$ is neutron flux (total path length of all neutrons per cm^3) and $\sigma$ is the fission cross section (dependent on neutron energy and isotope). With enriched Uranium, you raise the cross section by a large factor- U-235 has a fissile cross section of around 500 barns at thermal neutron energies, whereas U-238 has a fissile cross section of around 1 barn at thermal energies. But if you want to "fully" utilize the power of the U-235 (use a neutron flux that doesn't threaten the structural integrity of the vessel), you have a meltdown. Typical reactor cores operate at around 1000 degrees C. At this point, you are close to melting point for certain reactor materials and are most likely dealing with problems related to materials softening/weakening under heat. If you increase the reaction rate by 500x, you have a meltdown - the limit for our strongest materials is too low.
The US Navy uses high enrichment primarily for reactor longevity. They go 10-15 years without refueling, compared to commercial plants which are limited to around 2 years without refueling. They do this by using "burnable neutron poisons" which gobble up neutrons that originally had a chance of fission a U-235 nucleus. This allows naval reactors to put out a constant, high power level for 10-15 years, without melting down.
Lastly, U-235 is expensive. Market prices are hard to come by, but I've seen ballpark estimates of 15 million dollars per kg of U-235. This compares to 30-50 dollars per kg of U-238. Again, price-tag isn't as big of an issue for the US Navy, but for a power plant to stay in business, it needs to turn a profit.