What's most interesting to me are the things they agree on. Both are surprised to realize that the minimum wage economy for lack of a better word treats labor as fungible and vice versa. Employers are "always hiring" under the expectation that employees might not show up tomorrow for any number of reasons. Employees generally aren't invested in staying with a particular employer, like careerists would be. As such the undercover authors quickly shed the notion of filling out applications and take a more personal approach (taking above and beyond initiative). This fact also seems to be known by the for lack of a better word "minimum wage class", but it is obviously a surprise to the college educated authors.
I think the "nickel and dimed" problem comes from intermediate employers inserting themselves to remove this uncertainty. These are basically temp or daylabor agencies that charge a high fee (30-40%) to ensure that N number of people show up at the job. E.g. a contractor might need 10 people for 6 hours and pay the agency $10/hr (these were 2000-2005 prices) for a total of $60/person. The agency will deliver those workers in a van and charge for that too. Lets say a $5 van fee paid by the worker. So ultimately a worker might end up with $6/hr for 6 hours minus the $5 van fee minus $3 for the bus ticket to get to the agency for a total of $28 for the day (still 2000 prices).
Ultimately, the economic efficiency and therefore effective wage is low because lots of time is wasted waiting and traveling to random jobs. A "good job" in this regard is 40hrs a week, not going through an agency. The income here would be the full $10/hr, so $400/week.
The things they disagree on is what leads to the different conclusions because it begets different strategies. Ehrenreich starts with some "minimum standards" she believes that people deserve. This usually means renting a mobile home in a mobile home park on a weekly basis and getting a car. This eats up her entire income (coupled with a bunch of decisions that aren't exactly frugal ... like spending money on fast food because buying a frying pan is too expensive (yes, that's in the book!). She does eventually start shopping at Goodwill.) thus leading to the conclusion that the situation is inescapable: "People simply do not make enough with that particular "working/living"-ratio to get out of it. It's a trap.
Whereas Shepard is more hardcore (shops at Goodwill, walks 3 miles instead of spending $3 on the bus, washes clothes in the shower, ...you know the type

From a personal finance perspective, the Ehrenreich-type moves out too soon. Their reach exceeds their grasp. Signing up for rentals that cost 60%+ of their income, spending money on treats because they had a bad day, taking risks w/o having the savings by e.g. buying a car w/o having the means to maintain it. Basically trying to fly before they're ready to launch. The Shepard-type pinches their pennies and live below their means even when their means are tiny. They have a long-term plan, a strategy for getting there, and the will to sacrifice the short-term. In both cases it seems like the two types find their respective tribes, regarding the other tribe as either hopeless or privileged, respectively.
I think the disagreement comes down to attribution-bias and its reverse. Attribution-bias implies taking credit for one's successes while blaming failures on society. It's reverse---call it humble-bias---is giving credit to society or the team for one's successes while ascribing one's personal fortunes to luck. Different people have different set points for this bias, which comes down to agency. Still, even without this bias, my conclusion is that they're both right but right about different things. Thus the endless disagreements.
Ehrenreich is correct that low-wage labor is getting nickel and dimed. This is also Shepard's experience. However, Shepard shows that there's a way out of this trap (Cave?) by finding the people who have followed the strategy and following it himself.
There are thus two different solutions:
The individually-oriented one is to somehow teach people this strategy (aka personal finance)
The collectively-oriented one is to somehow get rid of the "nickel and dimed" system.
I expanded my sociological map a bit reading the two books. I recommend reading them side-by-side.