Brute fact is a close relative of uncaused cause, only the emphasis is on explanation rather than causation. Brute fact is a primary fact, one that need not be explained further, or on another reading self-explanatory. Uncaused cause is a prime cause, one that need not be caused itself, or self-causing if one prefers. If one thinks of explanation as building a chain of logical causations the difference disappears completely.
Therefore, declaring God or nature brute facts is effectively a statement of faith, or lack thereof. There is a long history of trying to justify the preference, the famous cosmological argument can be interpreted as an argument in favor of God being the "brute fact" or "uncaused cause". Swinburne starts his book by pointing out that such arguments are pointless because their premises are disputed. Even if we accept the principle of sufficient reason (and there is no sufficient reason for that) we still have a choice between infinite regress and first cause. Infinite regress was disliked by originators of Western philosophy like Aristotle, but there is no logical reason to reject existence of infinite causal chains, and hence eternal "nature". Then there is an insurmountable burden of identifying the first cause with God, even if nature is not eternal. In short, any judgement of what is a "better" brute fact will be based on person's emotional, social, cultural, philosophical, etc. preferences, and is purely subjective. People who like "closure" prefer God, people who like "diversity" prefer nature.
There was a similar dispute in philosophy of science about so-called analytic/synthetic distinction. It was about identifying "empirical facts" as opposed to "theoretical speculations", which could then serve as an undisputed foundation for science. It was on a much firmer logical ground, but still led nowhere, the distinction could not be made logically. The question of "final ground" for knowledge and explanations preoccupied philosophers for centuries and continues to do so. Hegel's Absolute Spirit, Husserl's pure consciousness, Heidegger's metaphysics of Dasein are the more recent entries to the list starting with God and nature. There are so many of them because there are no universally "better" ones.