It all depends on the type of juice you are using and the amount of calories consumed. Metabolism will generally drop when caloric intake is severely restricted. The metabolic rate will probably remain more constant with juice fasting, you will be getting calories in the form of carbohydrates and the body will not go into "survival mode" as quickly as it would on water only. In addition you will be getting vitamins and minerals from the juice.
Remember that water only fasting is about shutting down the body so it can heal itself. It is a rigorous discipline that needs to be carefully monitored when the fast continues beyond 7-10 days. If your lifestyle requires you to be active then juice fasting is probably the best way to go. You might want to throw in occasional water only days when you can stay at home and rest. You will be able to cleanse and detoxify your body. Then if and when you feel a water only fast is indicated, your system will be better equipped to handle the rigors of rapid detoxification.
Another thing is that from the body's perspective a lower metabolism is desirable. One of the chief aims of those interested in longevity is to lower the metabolic rate so the body does not burn itself out so quickly. The obsession with increasing metabolism is the result of our unhealthy eating habits, and the chronic problem of obesity that plagues our generation. We must choose between a healthy life style of low calorie intake and the standard diet of calorie rich foods. The healthier the diet, the less we need to be concerned with metabolic rate and the easier it will be to reach balance and health for our bodies.