Amazon vs. Walmart is an extremely interesting battle to watch. Amazon has massive advantages in technology; Walmart has massive advantages in size, distribution, and logistics. Amazon is gaining a lot of ground in the US; Walmart is much stronger than Amazon internationally.
If I had to place bets, I'd take Amazon in the long run. They're much more forward thinking and are playing a much more strategic game. Walmart has become overly reliant on price leadership and has had a very hard time orienting toward the future of retail. The Innovator's Dilemma will catch up to it eventually -- but it'll take awhile, because Walmart is so damned massive and dominant right now.