Its not meant to give "more power", its meant more balance the power out. When the bass hits, your lights dim b/c you are needing more than the alternator can provide for those few seconds. Then they come back on bright and your not using all the power the alternator can provide in the next few seconds.
Using 2 batteries, when the bass hits, power from the battery gives the amp (other electrical sutff) power for those few seconds and then recharges the next few seconds between bass hits, etc.
A battery acts almost exactly like a cap but better in my opinion.
I used 2 different batteries for over a year to power all of my equipment with no problems. I ran a 2 gauge power wire between the batteries with large fuses at both ends for protection. I also ran a 2 gauge ground wire to the body in the trunk and upgraded the wire that goes to the body from the battery under the hook to a 2 gauge wire. 2 gauge is bigger than what is coming from the alternator, but you are pulling power at 12 volts, whereas the alternator charges at 13-14 volts (whatever), more than 12.
Yes, 2 batteries will not last forever if you are constantly using more than the alternator can provide. But thats the key, you arent using more than it can provide most of the time. Running a big power wire between batteries helps, but wont solve the problem. Answer, another battery with shorter distance runs to the objects being powers helps mucho.
I believe they dont have to be the same battery, as long as they are both the same voltage of batteries (both being 12 volts). If you have one 12 volt and one 9 volt, then the situation you mentioned would occur. All the power from the 12 volt battery would try to travel to the 9 volt because its a lower voltage. (think of volts being degrees F, a higher degree will travel to a lower degree to balance out) If you have a large mass thats 70 degrees F and a piece of paper 70 degrees F, energy will not travel into the paper as they are the same temp....it doesnt matter that one has more total energy, just that they are the same.
I try to get technical and explain things, but sometimes it just doesnt work out right.
Anyway, I have done it and so have other for extended periods of time (1-2 years) without either battery dieing. I removed me 2nd one just because I removed my large amplifier and was not needed anymore. It actually still works and have used it to jump start a car before. The one in my car still works too, as I start it almost everyday.