TL,DR: You'll get a mass escape leading to a civil war that will result in the downfall of the government which set this up, and the rise of a 'rogue state'.
You're headed for trouble. You've filled a modern island city with the worst criminals you can find, have set them loose, and have given them a reason (forced sterilisation and incarceration in an unregulated environment) to be very angry with you.
The resources available in a city are substantial, and in the likely event that the prisoners organise themselves to escape, you could find yourself facing an army armed with whatever they can make in their city. Given near-future tech, which may include 3D printers, machine shops and whole factories, these probably won't be "improvised" weapons either.
I'll be the first to admit that there will probably be a large number of rapes and murders when the prison is first established, but these won't last. Humans instinctively organise themselves, and it is in the interests of the prisoners to exercise self-control. Those who can't will most likely be "selected against" sooner or later, leaving the more rational, organised criminals.
In order to prevent this, it will be necessary to have an extreme level of surveillance, and to be prepared to kill any prisoner who appears to be organising an escape, no matter how far in the future the preparations seem to suggest that the escape will take place. Even if you implant explosives in each prisoner while sterilising them, if you miss even a few prisoners neutralising their implanted bombs or tampering with surveillance devices, they'll eventually cripple your whole surveillance network and prepare their breakout unobserved. The level of surveillance required would be such that it would be cheaper to have a regular prison with guards on-site. Implanted bombs would also have their own political cost, and I doubt that a government sufficiently lax or deluded to think that this sort of prison is a good idea would go that far.
Additionally, in an area the size of a city, there will be ample opportunity for the prisoners to establish farms, thus securing their own supply of food. It is always possible for the authorities to simply destroy any farms they spot, but doing so would likely have consequences that the authorities were trying to avoid when they created this prison: the problems associated with expanding the range of crimes attracting the death penalty, and the monetary cost of supplying the prisoners with outside food as opposed to the political cost of allowing - or forcing - the prisoners to starve.
In such a situation, without adequate control of the prison environment, regardless of surveillance and remote prisoner termination capabilities, I believe that a successful mass escape is inevitable. The escapees won't necessarily include the insane or disorganised prisoners who cannot control their impulses, since these will most likely have been "selected against", so the escapees will most likely resemble something that you might call a "mafia army"; organised, disciplined and ruthless in a way that regular army recruits or volunteers are seldom capable of.
It is a fact that many normal soldiers, particularly conscripts, have difficulty killing another human. Normal humans are societally and genetically programmed against killing, and in combat, it is not unknown for a soldier to fail to fire or to deliberately miss. It takes quite a bit of combat experience (not just training) for a soldier to overcome this and to be fully effective.
However, this "mafia army" would already have been selected to include people who were either murderers before their incarceration, or who - due to the initially unregulated environment - have already been exposed to combat conditions. With even a few real soldiers included in the prison population, it can be almost guaranteed that the "Mafia Army" will be more effective than any unit of free soldiers unless those free soldiers also have actual combat experience.
The difference between this situation and other real prisons is that real prisons are either regulated internally by the authorities (e.g. Alcatraz), or if internally unregulated, the authorities can be confident that they have excluded any significant manufacturing capability and have control over supply.
Once an escape has been achieved, the escapees will likely be loose in sufficient numbers that recapturing them all - if they split up - would be a massive undertaking, and by retaining a degree of organisation, the escapees could act to secure their long-term freedom - by eliminating the government that imprisoned them in the first place.
Given that an escape may take years to organise, it is likely that the escapees wouldn't all simply go their own way once they were free - the prisoners who are likely to do that are also more likely to have transgressed against the prison's evolved set of laws and to have been disciplined or eliminated. This would leave the escapees loose in their parent society effectively as a guerilla army. With sufficient numbers, they could conceivably replace the government of their parent society with their own, or at the least cause internal strife for years to come.
Finally, don't think that because you've sterilised these criminals that they won't find a way to reproduce. Unless you castrate or spay them (physically or radiologically), effectively removing the testes or ovaries and potentially the penis or uterus too - with the attendant political fallout that will accompany the procedure - it is possible to reverse most methods of sterilisation, and you've probably included prisoners with sufficient education to perform such reversals, whether actually qualified or not.
Even if you really sterilise these criminals, and perform radical castrations with penectomies or hysterectomies with removal of the ovaries, it is not beyond the bounds of possibility (in a place as large as a city) that a few prisoners might not be able to perform stem-cell research that could result in restoration of these organs. Even if this doesn't happen, criminality is more than just genetics, it is also a mindset that can be instilled during childhood. If irreversibly sterilized prisoners escape, they could conceivably adopt children young enough to be sufficiently mentally malleable to be shaped into the next generation of criminals. Hence, while not genetically related to their adoptive parents, these children would still be the ideological offspring of their adoptive parents.
In the not unlikely event that criminals escaped from this prison take over the government of their parent nation, this nation would most likely come to be viewed as a rogue nation, on the order of Iraq (under the Hussein regime) or present North Korea. If this happened in a nation like the USA, it could end up as a global catastrophe...