"So it seems to have been well said that in Lacedaemon (Sparta) the free man was more free and the slave more a slave than anywhere else." Do you agree or disagree with this statement?

Well, this is largely an opinion question, asking for your judgment as to whether or not the quote provided is accurate. With that in mind, you also need to take into account that there are, in fact, two parts to this question: the first that free men are more free, and the second that slaves are more enslaved. Are both these points accurate?
As far as the second question goes, you'll really want to look into the history of the helots, around whose subjugation Sparta's entire society was based. Compare that with what you'd see in other polises (most famously Athens—Sparta and Athens tend to be natural contrasts), and you should be well on your way to formulating your thoughts on this answer.
The first question is trickier to consider. Keep in mind, Sparta was a very militarized state, but this militarization gave it almost a pseudo-communistic kind of approach. Is it overly harsh and dehumanizing, or does that harshness actually result, strange as it may seem, in a kind of egalitarianism? Also consider the political structure of Sparta and the role of the army within political decision-making. Is Sparta kingship or is it democratic, or is it both and neither? Really, this entire question is about making judgments, and what is most important here is that you think on these kinds of questions and form your own conclusions.