I think this has potential to be a crucial consideration with regard to our space colonization strategy

I see this raised often, but it seems like it's clearly the wrong order of magnitude to make any noticeable proportional difference to the broad story of a space civilization, and I've never seen a good counterargument to that point.

Wikipedia has a fine page on orders of magnitude for power.  Solar energy received by Earth from the Sun is 1.740*10^17 W, vs 3.846*10^26W for total solar energy output, a difference of 2 billion times. Mars is further from the Sun and smaller, so receives almost another order of magnitude less solar flux. 

Surfaces of planets are a miniscule portion of the habitable universe, whatever lives there won't meaningfully directly affect aggregate population or welfare statistics of an established space civilization. The frame of the question is quantitatively much more extreme than treating the state of affairs in the tiny principality of Liechtenstein as of comparable importance to the state of affairs for the rest of the Earth.

I currently would guess that space habitats are better because they offer a more controlled environment due to greater surveillance as well human proximity, whereas an ecosystem on a planet would by and large be unmanaged wilderness, 

Even on Mars (and moreso on the other even less hospitable planets in our system) support for life would have to be artificially constructed, and the life biologically altered (e.g. to deal with differences in gravity), moreso for planets around stars with different properties. So in terms of human control over the creation of the environment the tiny slice of extraterrestrial planets shouldn't be expected to be very different in expected pseudowild per unit of solar flux, within one OOM. 

if we can determine which method creates more wellbeing with some confidence, and we can tractably influence on the margin whether humanity chooses one or the other. e.g. SpaceX wants to colonize Mars whereas BlueOrigin wants to build O'Neill cylinders, so answering this question may imply supporting one company over the other.

Influence by this channel seems to be ~0. Almost all the economic value of space comes from building structures in space, not on planetary surfaces, and leaving planets intact wastes virtually all of the useful minerals in them. Early primitive Mars bases (requiring space infrastructure to get them there) that are not self-sustaining societies will in no way noticeably substitute for the use of the other 99.99999%+ of extraterrestrial resources in the Solar System that are not on the surface of Mars in the long run. Any effects along these lines would be negligible compared to other channels (like Elon Musk making money, or which is more successful at building space industry).

I may write up an answer because the question is interesting, but I think the premise of this question-- that we have a meaningful choice between planets and habitats-- is unlikely.

1. Assuming space colonization and terraforming get here before AI or other transformative technologies like whole brain emulation, it seems very unlikely that the terraformed planet will be "unmanaged wilderness". First, the Earth is already over 35% of the land area of the inner planets, so it's not like there will be a large amount of free space. Second, without the benefit of natural water and nutrient sources, not to mention hundreds of thousands of years of evolution to reach a stable equilibrium, wilderness will be necessarily managed to maintain ecosystem balances.

2. In the long run, planets are extremely inefficient as space colonies. It takes just a few years to disassemble Mercury into solar panels and habitats, creating thousands of times as much economic value as anything that could exist on the planet. Asteroids don't even need to be lifted out of a gravity well to be turned into habitats. So economic incentives will be strongly against planets, making the question moot. (Unless we turn them into planet-sized computers or something, which would again be out of scope of this question.)