Shares of Best Buy (BBY 1.06%) have come back from the dead this year, more than tripling since Jan. 1. Amazon.com (AMZN -1.70%) stock hasn't performed quite so well, but it has still grinded out a 24% gain for investors, besting the market yet again.

BBY Chart

Best Buy vs. Amazon.com YTD Price Chart, data by YCharts.

But these two retail titans are locked in a serious struggle for market share and mind share in the U.S. The bull thesis for Best Buy is that the company's price-matching policy and merchandising improvements will allow the company to win customers back from Amazon. In contrast, the bull thesis for Amazon is that low prices and free-shipping offers will convince many consumers to bypass brick-and-mortar retailers like Best Buy.

Right now, both companies' stocks appear to be priced for "best case" scenarios. Yet the best case for one is bad news for the other. As a result, I expect either Best Buy or Amazon -- and possibly both -- to post disappointing stock performances over the next year.

Best Buy roars to new highs

Best Buy investors are optimistic that the company's turnaround is sustainable.

On Tuesday, Best Buy hit a new multiyear high above $40. While the company has not yet returned to comparable-store sales growth in the U.S., flat comps (as reported last quarter) are a big improvement for Best Buy.

This month, Best Buy shares have been boosted by reports that the company is finally turning the corner. Investment Technology Group claims that Best Buy could report a 3% to 5% increase in same-store sales for the current quarter, due to better sales of big-ticket items that cost $1,000 or more.

Until recently, Amazon had a big advantage over Best Buy with big-ticket items. First, Best Buy's decision to match Amazon's prices has its biggest impact on expensive merchandise, where price differences are likely to be largest. Second, sales tax can be a significant extra burden for big-ticket items. With Amazon collecting sales tax in more and more states, this advantage compared to brick-and-mortar retailers is disappearing in much of the U.S.

A separate research report from Stifel Nicolaus found that an increasing number of Americans plan to shop for electronics at Best Buy in the next few months. Widespread optimism that Best Buy is bouncing back has driven shares back to a healthy valuation of 17 times current-year earnings estimates.

Can Amazon win big?
On the other hand, the bull case for Amazon is predicated on a continuation of its rapid revenue growth. This is demonstrated by the company's heady valuation of more than 100 times forward earnings.

Amazon investors are betting that the company will keep growing rapidly for a long time.

In the first half of 2013, Amazon's North American revenue grew by 28%, or $4.1 billion year over year. And 70% of this revenue growth (or $2.9 billion) was attributable to the "electronics and general merchandise" category. In fact, the electronics and general merchandise segment has been Amazon's most important growth driver for many years now.

Clearly, a good portion of Amazon's growth in the electronics and general merchandise segment has come at Best Buy's expense. The flip side of this is that if Best Buy is finally holding its own -- or even retaking market share -- it will be virtually impossible for Amazon to live up to investors' optimistic growth assumptions.

Foolish bottom line
A few recent research reports suggest that Best Buy is on the mend, and may have already returned to comparable-store sales growth. If Best Buy's restructuring is allowing it to compete effectively with Amazon, then the recent Best Buy stock rally may be sustainable.

But if that's really true, then Amazon investors will be in trouble. Obviously, Best Buy is not going to destroy Amazon, but the company's current stock price only makes sense if you believe that Amazon will trample Best Buy and other big-box retailers and become the go-to place for electronics and other major purchases.

In other words, either Amazon bulls or Best Buy bulls will be proven wrong in the near future. In fact, it's possible that both will be proven wrong -- that Amazon's growth will slow while Best Buy continues to struggle. As a result, both stocks are potential short candidates as we enter the holiday season.