This is a bit of a false dilemma, mostly because it precludes the option that both can be true ('depending on the context', of course). Structural explanations do not exclude "Great Person"-explanations. More likely is a systemic relationship rather than a causal one. The extraordinary achievements of any "great" person tend to be dependent on more structural processes leading to circumstances which enabled them to accomplish whatever it is that made them "great".

A more historiographical point of view is that both can be true, depending on how the historian structures the arguments and interprets the evidence. I could write two histories of the second World War, one explaining the events in terms of human/individual action and the second explaining the war in terms of socio-economic structures, and both would be more or less equally "historically accurate".

On a more metahistorical note, philosopher of history Eelco Runia has noted (as have others before him, but his popularized the issue in recent times) the use of metonymia by historians. For example, stating that 'Napoleon defeated his enemies at Austerlitz' is as historically false as well as historically true as stating that 'France defeated Austria at Austerlitz'. You could interpret the former as an example of "Great Man Theory" and the latter as a more structural statement, but both are narrative shortcuts through metonymia.

But I have digressed at this point.

I personally believe that Adam Ferguson had it right when he noted that social reality is the result of human action, but not of human design. The past is, by and large, a neverending and interrelated string of unintended consequences and events. Us historians attempt to explain these events and processes, we try to shape narrative order to chaos and, admittedly, we learn a lot in the process.

Even though every historical narrative is, at best, limited and a fiction at worst.

This topic came up two days ago: http://www.reddit.com/r/AskHistorians/comments/31lqtt/what_is_great_man_history_what_are_its_pros_and/

Personally, I go for a bottom-up mode of history. I posted an answer here about 'Great Man theory' and its pros/cons. Hint: there aren't many pros.

/u/TheShowIsNotTheShow also explained it really nicely in that thread:

the biggest downside to 'Great Man History' is exactly the erasure of anyone except the great men.

I've put a lot of my focus on the Civil Rights movement, and this is the big problem there with MLK. It's also the issue with the Napoleonic Wars, and numerous other times and places. It changes huge movements for social or political change into something that was the result of one man. In actual fact, they generally have a lot of people behind them that you don't know about. I feel like I'm talking about the CRM on here a lot lately, so I'll let some one else expand upon this with their area.