Deep cycle is always better for car stereo applications
a normal battery when brought below 11 volts will slowly start to accept a lower amount of charge an after bringin it below 11 volts too many times the battery wont accept a charge at all.. but a yellow top deep cycle can be completely killed down alot of times an still accept a charge
lets say for instance that ur car is running ur two L5's an you have about 1500rms going to them an your stereo is turned up to like 40 an you have some bass hittin hard an while this bass is hitting it brings your battery below 11 volts just for a second then the hard bass is done an two seconds later it comes back an brings that battery below 11 volts again so after sitting there doing this for a while your battery would have been brought below 11 volts alot of times so then when you turn off your car its possible that since you brought it below 11 so many times that that battery stopped accepting charge so when you turned it off it was sitting at like 10 volts an the next day you walk out to turn on ur car an you dont have the between 11.6 volts an 12 volts that it would take to crank ur ride ( it might not go out the first time you do this but a couple of sits in the car an it will happen ) but with a yellow top it wouldnt have stopped accepting a charge because they are built for the abuse so as long as you let ur ride idle a little bit with ur stereo off before turning off the car then you should have no problems
Ok, the reason I disagree with GlassWolf here, is unless you're using the type of isolator that completely seperates the circuits (i.e. not the relay type a lot of people use), then you're still going to end up dropping your starter batteries voltage below 12 volts and damaging it, if you're pulling a lot of amperage..which in turn, will end up destroying your alternator, and even your deep cycle battery too, in time. (Even deep cycles have a limited number of discharges before they're toast.)
Also, isolators like that arent exactly cheap. Especially not ones meant to handle high amperage situations.. It's actually cheaper to buy a pair of deep cycle batteries, than an isolator, and a normal starter battery. And wired in para this also presents you with more CCA than a normal starter battery would, as well.
Also, using a solenoid isolator (the type I believe Glasswolf is referring to), you will experience significant voltage loss, as the resistance is normally above 15 ohms. (in most cases you'll lose over .5 volts - in high amperage situations, even more)
Disadvantage to this, however, would be if you plan on playing your stereo with your car off for any period of time. Using the isolator, would guarantee your starter battery dosnt get touched.