I believe the 'big questions' are the ones that have been around since the dawn of civilization and are still pertinent today. What happens after we die? Does God exist (and for that matter, which God?) Are we truly free or is the path of our lives and our decisions somehow predetermined? However, questions like these will always remain a matter of faith and are difficult if not impossible to 'resolve' philosophically due to their expansiveness and impenetrability.
Well, then, we have our first disagreement. I hold that the "expansive and impenetrable" Big Questions are indeed soluble, they are merely recondite. It took man fifty thousands years to crack the atom, but, he did it. Whether it can be done within the span of this conversation, or in another fifty thousand years, we will crack the problem of the liberty of the will.
In fact, I will go further. I am a Catholic Fremen, and I have zero faith in the existence of the One, Cardinal Cusa's (1401-1464) term for "God". I know the One exists; I have faith not in His existence, but, rather, in His character. But, even this an ongoing process of strengthening of faith to the sticking point of irreversible certainty.
I disagree with your suggestion that progress in philosophy is analagous to progress in science, for the reason for the impenetrability of some of the Big Questions is that they are largely non-empirical or metaphysical matters that exist outside of our observation and thereby outside of the purview of science. The ancients may not have been able to anticipate putting a man on the moon or splitting atoms, etc., but that is merely because that had neither telescopes nor microscopes that were powerful enough. With the appropriate level of technology, our observations and therefore our knowledge of natural phenomena are uniform, for if anyone disagrees it has only to be demonstrated to them empirically. Everyone then sees the same thing and that is the end of the disagreement. Secondly, the problems of science are discrete while the big problems of philosophy are often expansive, meaning that in one case the parameters of the investigation can be sufficiently narrowed to guide its scope and its progress, while in the case of philosophy it is much harder to arrive at a standard set of 'common denominators', (such as, if we were to ask 'What is the meaning of Life?') partly for reasons that I will explain shortly. I would also point out that knowing-how and knowing-that constitutes two fundamentally different types of knowledge, each with its own distinct set of hurdles.
In contrast, the problems that I mentioned have several different camps or schools of thought in approaching these problems, though not everyone can conform to the same agreement no matter how passionately they argue, or how valid their logic is, or how sharp their reason is. I will therefore assume that their powers of deduction and observation are roughly equal, or that there exists proponents from each major camp that can contend on the same level (and it is difficult to see how any advances in science and technology could help them to better see what could not be 'seen' in the first place). I believe much of the disgreement lies in the ordering principles, or first principles that people have, which form the starting point or framework of their arguments. These first principles are non-negotiable and cannot easily be overturned because they are imbedded into their very way of conceptualizing the world. They appear to be necessary for any undertaking that is not merely empirical (and perhaps even for those that are). When debates unfold, the bulk of the argument crystalizes around these starting points ad hoc and it is these provisional extentions that do battle with each other, often going through cycles where discrete pieces of the argument of both sides are challenged, 'refuted', refined, and counter-argued, while the central core remains unchanged, indemnified (as opposed to the 'domino effect' analogy that supposes that if one supporting premise is undermined, the whole position is demonstrated to be false).
The belief or "knowledge" of God versus atheism is the classic example of this because for strong believers or disbelievers the existence or nonexistence of God is so fundamentally a part of their way of being in world that is not possible for them to conceive of the alternative through this mindset, and indeed, for some it cannot be a mere belief -- an idea that is autonomous chosen instead of its mutually exclusive oppposite, as if either might be true -- but rather that they "know" it as surely as they "know" the heat of a hot summer's day.
Now we can both see how this 'problem' has been 'resolved' for the one person, or a group of people of a particular creed, but this is not what I meant when I said that some of the Big Questions of philosophy are difficult to resolve in general, in the sense that we can all close the book on them having finally put the issue to rest for everyone who might have an interest in the subject and is seeking a single answer. I am reminded of the absurd humor of the The Hitchhikers Guide to the Galaxy where finally it is revealed that the answer to the meaning of life is "42", as if we could attain such answers to the ultimate questions once they can be computed by the most advanced artificial intelligence over a period of 10 million years.