Thank you, everyone.
I never expected such a large amount of thoughtful advice regarding the state of the trees. Thanks all.
I don't think I have any 'before' pictures, but I will look
I can say that they did not spike these trees... I believe they had a truck with a platform for both of them.
As far as the tree locations, the one between the two houses is actually splitting a shared asphalt paved driveway ( I know, probably not good ) :\ It has a very small amount of dirt about the trunk before the blacktop starts.
The second tree is in the front yard, just before the front yard begins to slope. The slope is appox 60 degrees towards the sidewalk for about 6 feet. Unfortunately, that is not the end of the story. Previous to our having moved in, the neighbor cut a new driveway on his side. The new driveway was about 6 feet from the trunk, but I could see that the guys who did it cut a lot of roots. I had an arborist come out to have a look who suggested feeding the tree. In general, they tree's health looked good to him, although he was not happy about the roots at all.
There were mixed opinions on whether I should further cut the trees to correct any problems so not entirely sure what to do there, but, I would rather not shock them anymore... My biggest concern was any rot issues that might arise from improper cuts. I also don't want the original company to come back out to correct things, since now they seem like possible clowns and I don't want them making things worse.
I guess I will see if I can get an arborist to have another look. So, the lesson of the story seems to be make sure the guy cutting is a licensed arborist and make sure they are following ANSI standards for pruning.