An interesting question. A decade ago A.T.Kearney really was a top top strategy brand in most people's eyes. Just below MBB but right there with the likes of OC&C, Marakon (as was), Monitor, Arthur D Little, etc.
In the intervening years there was a lengthy period where ATK was part of EDS and that inevitably took some of the gloss off the brand; they just struggled to break with the stigma of "how can you be providing independent strategic advice when you have EDS services that you must be under pressure to sell into your clients?"
Now they're independent again and working to regain lost ground; my impression is that you'll find the quality of projects to be top tier there, it'll just take a while for the brand to regain its former sheen.
As regards Accenture, the strategy team there are highly regarded and I believe have entry criteria akin to a top tier strategy firm. Those in positions of importance (to your career) at both corporates and with recruitment firms would certainly look favourably on someone who's done a stint in strategy at Accenture. Personally I know a couple of people who've been through that route; one's gone on to be successful in investment banking and the other to be similarly successful at one of the world's most prestigious internet companies. Neither of which is a shabby outcome and pays testimony to how strategy at Accenture is viewed by those who matter (to your career).
I guess whilst not coming down in favour of either one, I'm saying that you'll not be dropping a clanger by joining either of these practices. So I'd base your decision on the interactions you actually have with the firms, how much you warm to the people and the pipeline of work / client list they currently have in your practice area.
I can't comment specifically on strength in Oil & Gas, but hope the above is helpful.
Best of luck in your interviews.