Our club now has three oak barrels, and while at least one is going to be dedicated to a solera, we'd like to try a couple other brews before we resort to two more soleras.
Barrels are known to let oxygen in, good for the bacteria we'll have in our sour, but is this simply a flaw in every other regard, or does it contribute to any desired characteristics?
Oxygen in and of itself is a staling agent, plain and simple. Some styles benefit from being a bit stale. For instance, here in the states, what we know as "British" beer is typically a bit stale simply because by the time it gets here long after being brewed and having crossed the sea in a hot ship, it's not exactly fresh. So if you want to clone your favorite, say, ESB, then a bit of staling will help get you there.
Now, barrels don't exactly let oxygen in the same as if you left the beer exposed to air, or if you didn't fill the barrel completely. What they do is allow the beer (or wine) to micro-oxidize. Search the web for info about micro-oxidation and you can read lots of fun debate from the winemaking world about how it's either beneficial, bad, non-existent, or maybe no different than regular oxidation.
A bit of oxidation is usually part of an Old Ale.
I think more important than whether a beer will benefit from oxidation is whether the flavor of the beer will benefit from being aged in an oak barrel. I think that the flavor of the oak is going to outweigh the flavor change of oxidation.
In that case I would look at commercial examples that are oaked or aged in oak or bourbon barrels such as Founders KBS or Weyerbacher Insanity. One is an RIS with coffee and vanilla, and the other is an English Barleywine. Both benefit from the oak flavors, and with such intense flavors to start with, oxidation is not as big of a factor.
Old ales, barleywines, stouts, porters, and generally anything you might age will benefit from aging in an oak barrel.
Besides old ale, barleywines benefit from some oxidation.
