Well one thing that does greatly affect the battery is the connections throughout the charging system bec rust or corrosion will cause a current loss or drain or strain on the battery , starter and alternator.
Most of the newer vehicles are designed to regulate the alternators output current and battery output current via a built in voltage regulating circuit inside the comp system, some vehicles have used internal voltage regulators built into the alternator and some use external voltage regulators.
Even though a battery for example is rated 12 volts in fact any good battery with no draw or the engine off gives out closer to 13 volts and the alternators on the average give out close to 13.7 or almost 14 volts.What you have to keep in mind here is that any current draw or load on the charging system uses up voltage so really with different devices on the alternator might be turned on just due to current or load draw on the battery.
One main factor of any battery is dead cells bec after time all car battery's end up with dead cells and these dead cells will weaken the battery and cause the alternator to have to engage it's output circuit more often then normal , plus if you add weak or corroded connections into the picture the whole system in fact has to over work.Some times after driving up and down hills or after a vehicles battery acids are shaken up some and then the vehicle is parked or turned off the engine might not want to turn over properly just bec these dead battery's cells and allowing the battery to sit awhile at these hard start times can help it to allow it dead ells to settle and suddenly the vehicle starts with no problem.
Yes a higher output alternator can charge a battery faster but it could over charge it too unless it has a charging system that constantly monitors and regulates the current etc.You need to remember that when any vehicle sits idling or isn't been driven at hwy speeds that the alternator really doesn't get to charge the battery fully and actually you should drive at least once a wk on the hwy for a good 10 to 15 mins to actually keep the battery up.
My basic rule of thumb is if any battery is drained down so low that it doesn't even turn over the engine properly or is dead and requires a boost or recharging you're in fact weakening and damaging the battery , plus do it a few times and the battery will be basically toast or it will loose most of it's cells capabilities to hold a charge or be full of a lot of dead cells after wards.
Hope that helps and best of luck.By the way one reason they designed vehicles with voltage regulators is to regulate and for less chances of over charging or over drawing the battery.
One basic thing I recommend besides cleaning and protecting the charging system connections etc is to know how many cold cranking amps your starter requires to turn the engine over properly.You might be surprised to hear that a full size 8 cylinder engine might only require 165 cranking amps to turn it over fully and many of today's smaller engines take a lot less but my rule here is to have a battery that is rated a good 5 times more in cold cranking amps then it takes turn your vehicles engine over properly.Mainly I recommend a good 750 or 850 cold cranking amp battery is bec in the hotter and colder months a battery can loose even more then half of it's rated cranking amps and then you have to consider just how important the rust or corrosion issues.