Neither is a scenario you want to have happen to your batteries as it will probably shorten the lifespan of both and could create a potentially create a dangerous situation if one battery gets severely overcharged. Wiring batteries together in parallel has the effect of doubling capacity while keeping the voltage the same.

Wiring Your Battery Bank In Parallel
What happens when you connect batteries in parallel. In short when two non identical batteries are connected in parallel current will flow from higher voltage battery to lower voltage battery. The same is also true of batteries that are identical in every way except that one battery is older than the other. The basic concept is that when connecting in parallel you add the amp hour ratings of the batteries together but the voltage remains the same. When you connect two batteries in parallel you are able to double the capacity amperage rating while maintaining the same voltage. Connecting in parallel increases amp hour capacity only. Which is not good.
When you connect two identical batteries in parallel you double the output capacity while keep the output voltage the same as either battery. Small voltage difference between these two batteries can balanced but if voltage difference is high it may destroy lower voltage battery. In the other case if two identical batteries are connected in series the output voltage is doubled but the output capacity is kept the same as either battery. Two 6 volt 45 ah batteries wired in parallel are capable of providing 6 volt 9 amp hours 45 ah 45 ah. One 12 volt 10ah battery one 12 volt 10ah battery connected in parallel equals 12 volts and 20 amps.