How would the criminal justice system be different if federal laws were enforced by state court systems?
It is likely that there would not be any major differences if this were to happen.
It is possible that some differences would be seen if the federal laws were to be enforced by the states. This would be particularly true if the federal government did not fund the states to help them pay the costs of their new duties. This would mean that much less enforcement would happen. It is also possible that some states would not try very hard at all to enforce certain federal laws. For example, Washington and Colorado have passed citizen initiatives legalizing the use of marijuana. Such states would surely not enforce federal laws on that subject.
On the other hand, however, it is likely that the bulk of the business of law enforcement would not change. Most federal laws do not deal with issues that are particularly controversial. As long as the states were adequately funded, they would simply enforce the laws the same way that the federal government does. State law personnel are professionals and would enforce the federal laws just as they enforce current state laws.
So, there would probably be some differences in a few areas of law but, for the most part, little would change.