how the heck do you decide which method to use
Really its up to you!
I think traditionally this was based on whatever method people in the region built with. People that live in regions where earthen construction is the dominant (or only) form of construction have been familiar with a method since they were children. If bricks are used in the area you use brick, if cob is used you use cob, rammed earth you use rammed earth ect, ect.
That being said I would say cob is slightly "faster" than any other form in the essence that the building material is going straight to the wall and drying there using no form work. However when you are building free form you have to make sure you are building plump (plumb
ha ha) walls.
I would argue that adobe bricks are more diy friendly in that they are "easier" to keep plumb and straight although this method is a bit more labor intense. You have to make the bricks, let them dry, stack them near building site, then place them to build wall. The building material is handled more times than cob.
I know it must depend on the resources available
Usually all material required for earthen construction are close to a build site. With the exception of some parts of Florida? Clay is found in abundance right at the build site and sand can be found close by if not on the build site as well.
but is one better than the other for say thermal qualities?
No, all earthen construction carry's the same thermal qualities all things being equal.
Cob is partially mud (I believe)
Cob (and all earthen constructions) are an approximate ratio of sand to clay usually 70-80% sand and 30-20% clay and straw around 10-20%. As a side note cob construction is really the only method requiring straw in the mixture. Adobe bricks do not require straw but is optional.
How does that handle rain, hail or other weather?
Quite well! Depending on annual rainfall and how much the roof overhangs to reduce exposure to weather and how high off the ground the earthen walls are.
And how long can they last?
As long as it is maintained, a very long time. There are cob homes in England that have been continually inhabited for 400, 500, 600, 700 + years. Taos Pueblo has been inhabited at least 550 years and possible as long as 1000. Shibam in Yemen is at least 500 years old. So quite a long time, as long as they are built correctly and maintained.
Are there builders out there who can help us achieve something as nice as the home in the link below
I'm sure there are.
Can walls be repainted?
Yes as long as its a lime based paint or a paint that will "breath".
Is a thatched roof practical in the US?
Practical? Its possible
but I don't think it's practical as its not something that many people in the US know how to do (that I know of). In England there is a tradition of thatched roofs and still tradesmen that know how to maintain and build new thatched roofs. I think a tiled roof would be more reasonable to do.
Thanks for the help
I feel like I don't know where to begin
This is a good place. I would read all the posts in the cob forum. Another good place is your backyard. Dig up some dirt mix it with water to a moldable consistency and make some bricks, let them dry. Do some drop tests, leave them out and see how they do in the weather.