If I hooked two 12VDC deep cycle batteries together in parallel, one having a higher voltage, would there voltage equalize?

 

Theoretically, the higher voltage battery would discharge in the lower voltage battery until both voltages are equal.
Practically, if the voltage difference between the two batteries is high then the a high current will flow, the batteries will get hot and may explode. In this way, you degrade the battery's life because you overheat it.
What is more, if they dont have exactly yhe same thermal characteristics then there will be a small voltage difference between them and a current will flow and discharging one in each other. Also, if they dont have exactly the same internal resistance the battery with the higher internal resistance will discharge less and thus having a greater voltage than the other battery , thus a current will flow between them when you disconnect the load.

It is better you connect their negative poles together and put a diode on each positive pole with its anode connected on the pole. Then connect the diodes' anode together and you have paralleled batteries which cant exchange charge between them and cause problems.

 

Amplepower.com has some interesting things to say about paralleling batteries.

 

I have four brand new deep cycle batteries. They are the same brand, same size and were bought at the same time from the same store. I have put them in a cabin to hook to a inverter and a charger. I will only charge them when the voltage drops to around 12.5 and use the inverter maybe every night. I charged the four batteries individually to full charge with what I think is a decent digital charger and then hooked them all together. A coworker of mine was telling me I need to hook them all together and then charge them to "equalize" them as one battery. Of course I am going to charge them all at once from now on but I thought that hooking them all together would automatically(over a little time) "equalize" them. He was trying to tell me I did something wrong and that I don't know how batteries work and that he is the greatest and I am the worst. I told him that if one was a little lower than the others that they would even out just by all being hooked together. He said I needed to study batteries because I didn't know what I was talking about. Maybe I'm wrong but I don't think that charging them all at once is going to do any better of a job of "equalizing" them then charging them individually first then hooking them all together would. Especially since I plan to charge them all together quite a few times in the next two months. I read something about equalizing cells in a battery by over charging the battery a little to make sure all the cells are fully charged. I can understand that and if I had hooked these batteries in a series then it might have done some good. Any opinions?

 

I have used lead/acid batteries in all kind of connections, 6+6+2,12's in parallel ,6's deep discharge in series, mostlly in recreational vehicles, and all worked. my suggestion do not mix old with new, use same capacity for all & individuall charge all batteries before connecting.