Nothing really pins you down to one choice or the other, except the choices you've made for yourself in the past. Have only 12V inverters and you don't want to upgrade? Then you're not going up to 24V for a while... On the other hand if you get greedy and money is no object, then winding for 48V and getting the extra batteries and new fancy inverter is not an issue. That's really just your choice.
As for getting more power: Add up the electrical losses in your system, and factor out the ones that don't have anything to do with current (there aren't many). This is where going to a higher voltage range offers the most benefits. Getting an alternator to produce 1000Watts at 12V, 24V or 48V is virtually a coin toss question. Change wire, change number of turns, presto. But getting the power OUT of the turbine, down the tower, along whatever cable along the ground you have, push thru a rectifier block or two, and into the batteries - the whole long winding road is what makes the difference. If there's a 0.05 ohm resistance on that path, then the 80 Amps or so that you need to carry from your 1000 Watt genny will shed about 1/3 of the power as heat in wire! The same cables hooked up to a 48V mill only needs to carry 20 amps or so, and the same cable size will lose only about 2% of the power as heat.
Any resistance in the cables connecting the genny to the battery bank will have an effect on the turbine, too. Tends to make it turn faster, the greater the resistance is (I will skip the details of that to not drift off topic).
I figure if you've got your 12v turbine already, have fun with it first!
If you're like me, getting the most out of the first turbine will be a vocation all of its own (and then you'll better appreciate the benefits of going up in voltage or improving what you've got).