What parts root better? Last year's growth or 2 year old (older branches)? Now that my garden is littered with fig tree guts, which parts do better? 

For me it is the ones that were facing the sun, they seem to have more energy.
The next would be the older wood.

I think older wood is best but any hardened off wood is fine. Clearly, people here prefer tips.

Hi LizzieB,
Put them all in the ground - give them a chance- you can always pull some out if there are too many.
For me the most important is not the age but the length. 20 cm / 3-4 inches and most of the stem underground for it to keep its moisture. Else they desiccate too fast and can't root.
Another point is they should get sun to get warmth - if they are in a cold and shadowy spot, they are going to have a bad time rooting and growing properly.
At this point of the year, all wood on your ground is at least half hardened and this is enough to get it to root. Get ready to leave in a forest :) .
I would put them 4 by 4 at 50 cm of distance for easiness of moving them around later .
I would try some in pots for having a definitive place later - did I mention my Dalmatie cuttings in pots - 3 pots already and I already saw some root shoots that will go in pots as well for exchanging or winter backups or just
for testing the pot culture.

tip cuttings definitely make better looking trees. however, i'm not very good at rooting tip cuttings. i always cut them off. something to do with some hormone in the tip bud that is preventing cutting from leafing and rooting quickly. dormant wood taken during the winter and shipped right away is the one that works best for me. even if the wood is slightly hardened and have some green to it, is better than any soft green cuttings. usually 1-2 yr old works the best. 

Well thank you Pete from NC and everyone thank you so much. I'm learning every day.
Going to make the best of this little monster and see if we can't get a bunch of Figlings / Figlets?
She's been so good for so many years. I can't wait to take some pictures.