With the past subjective for the comparison, the alternative is a hypothetical (not real) situation:
- They couldn't do as much as they would have done [under some condtion].
With the simple past for the comparison, the alternative is some real situation previous to the one under discussion:
- They couldn't do as much as they did [at some other time].
There are two things that make your specific example of "like" tricky:
"To like" is not an action verb, so the exact moment that they formed the preference to go a particular speed doesn't change the meaning that much:
- They couldn't go as far as they expected to. Expectation was formed before the going. The result was unexpected, but only compared to the previous expectation.
- They couldn't go as far as they would have expected. If they had thought about it beforehand, they would have expected to go farther, but they didn't think about it in advance.
The other thing that makes this tricky is that "as X as you like/want/please" is an idiomatic expression meaning that the amount of X is not limited by someone/something else. "You can drive as fast as you like" does literally mean what it says, but the implication is that nothing is limiting your speed:
- They couldn't go as fast as they planned. They made the plan before going, and something prevented them from following the plan, like "attracting too much attention".
- They couldn't go as fast as they liked. They had to obey some constraint that made them go slower. Doesn't sound like they actually formed some preference in advance because of the idiomatic meaning.
Your second example sounds like, "They couldn't go fast for fear of attracting too much attention." It doesn't actually sound like a comment on their preference like the first sentence does.