Since the turn of the year, shares in Morrisons (LSE: MRW) and Sainsbury’s (LSE: SBRY) have risen by 29% and 14%, respectively. This may be somewhat surprising given that the outlook for the UK supermarket sector remains highly challenging. After all, with Brexit on the horizon, interest rate rises ahead and the threat of Aldi and Lidl still strong, it would be unsurprising for Morrisons and Sainsbury’s to see their valuations fall.

However, both stocks have the potential to double in value over the medium-to-long term. That’s due in large part to their strategies. While very different, they have the scope to turn around years of decline.

Reconnecting with customers

In terms of Morrisons’ strategy, it’s reverting to its core operations as it seeks to reconnect with old customers. For example, it has sold off its convenience store operations and scaled back investment in non-core areas such as online in favour of focusing on traditional, good value products that resonate well with its target customer base.

Furthermore, Morrisons is making major efficiencies and reducing costs as it seeks to become increasingly competitive on price. And with it leveraging its status as a major food producer through the deal to supply Amazon Fresh, Morrisons seems to be making the right moves through which to deliver rising profitability.

Diversifying for growth

Although Sainsbury’s is moving in a different direction to Morrisons, its strategy also appears to be sound. For example, it’s in the process of purchasing Home Retail and having the Argos brand within its asset base should allow Sainsbury’s to tap into significant cross-selling opportunities. It intends on having Argos concessions within Sainsbury’s stores which should boost click and collect sales, while Sainsbury’s focus on a simplified pricing structure should also help to improve customer satisfaction and boost sales.

In terms of their valuations, both Morrisons and Sainsbury’s offer substantial upside. For example, the latter has a price-to0earnings (P/E) ratio of 13.9 and this indicates that there’s plenty of scope for an upward rerating. However, with Sainsbury’s forecast to grow its bottom line by just 2% next year, the chances of its valuation doubling over the medium term appear to be less encouraging than is the case for Morrisons.

That’s because Morrisons is expected to record a rise in its bottom line of 44% this year, followed by further growth of 10% next year. This puts it on a price-to-earnings-growth (PEG) ratio of only 0.4 and indicates that Morrisons has greater capital gain potential than Sainsbury’s.

Certainly, it will take time for them to mount full recoveries and they’re at the start of their comeback journeys. But with sound strategies, low valuations and growth potential, both stocks could double over the long run. And with its superior growth outlook, Morrisons seems to be the more likely of the two to reach that point first.

Despite this, there's another stock that could outperform both supermarkets in the coming years. In fact it's been named as A Top Growth Share From The Motley Fool.

The company in question could make a real impact on your bottom line in 2016 and beyond. And in time, it could help you retire early, pay off your mortgage, or simply enjoy a more abundant lifestyle.

Click here to find out all about it - doing so is completely free and comes without any obligation.

Peter Stephens owns shares of Morrisons and Sainsbury (J). The Motley Fool UK has no position in any of the shares mentioned. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors.