Sears is not dying or dead. They have around 40 some brands they own and they are doing quite well. Yes they aggressively close non performing stores and they aren't in every mall like they used to be. But they are very much into ecommerce, supply chain management, repair business etc. and the technology groups they have do some neat shit, again not a panacea but pretty cool.
Also remember they are in the top 20 of all retailers in the US so if you can say you worked on ecommerce for a top 20 retailer and made real impacts, sorry that to me will be better then Deloitte. I'd hire a person with that experience over the consulting person, especially for a online business.