This is, of course, a matter of conjecture because we cannot know what would have been. However, I think you could argue that our criminal justice system would be more of a patchwork than it is now. There would be states with much more or much less in the way of protections for defendants than is currently the case.
I think that more aspects of our system would resemble the death penalty -- with wide divergence among the states. We currently have states with and without the death penalty. We have states with the death penalty that execute relatively few people and states that execute many. This is partly because the federal government has stayed out of it and let the states have a great deal of leeway.
So I think that we would have more of that. We would have states where the exclusionary rule would be weaker or even nonexistent. We would have states where there would be more (or fewer) exceptions to the rule requiring a warrant for searches.
Without the federal court system to oversee the states, I think that there would be more differences among the states with more conservative states being much "tougher" than more liberal states.