There are isolators, and there are relays. An isolator does just that, isolates the front and rear batts 100%, for charging and discharging. A relaying isolates the front and rear batts when the ignition is turned off, and connects them when it is turned on. Each type has its benefits and drawbacks.
Isolators' benefits include allowing completely different batt types/sizes/ages/conditions between the front and rear, and of course the ability to run the stereo with the engine off with no conern for draining the engine's batt. The drawbacks include the price, higher than a relay by about double usually, and obviously more expensive than running nothing at all. Usually around $100. An isolator also adds a slight resistance to the circuit. Older isolators use to suffer relatively large voltage drains (a volt or more), but newer ones display much less resistance. Still, more than running nothing at all.
Relays work by making or breaking the circuit between the front and rear batts, triggered off a signal wire from the ignition. When the ignition if off, the relay's contacts are open, and the rear batts are isolated from the front. This allows engine-off play time with no concern for draining the engine's batt. When the ignition is turned on, the circuit is made between the front and rear batts, and they charge/discharge as one large battery. This has the advantage over an isolator of allowing the capacity of the batt(s) under the hood to be included in the stereo's consumption, when the engine/ignition is turned on. The disadavantage is, because the batts are much of the time wired directly together in parallel, the batts must be of very similar type/size/condition to allow for an even charge/discharge, and not promote parasitic discharge due to varying internal resistances. A relay is the medium priced choice, at around $50-75.
Last option is runing no isolation device at all. This is like the relay description above when the circuit between front and rear batts is made, all batts are wired together in parrallel and act as one large batt. The advanatge of this is, obviously, the cost. Zero dollars brings it in as the cheapest option. The disadvantage is, like the relay setup, all batts in the circuit must be very similar for optimum performance. The other disadvantage to no isolation device is that you can run your engine starting battery dead while playing your stereo with the engine off, leaving you stranded and wishing you'd opted for choice number one or two.