Maybe Wall Street should be called "Weed Street." Big Canadian marijuana grower Canopy Growth listed its stock on the New York Stock Exchange (NYSE) earlier this year. Now it's about to have company. Aurora Cannabis (NYSE:ACB) begins trading on the NYSE on Tuesday, Oct. 23. Aphria (NASDAQOTH: APHQF) filed last week to list its stock on the NYSE.

It's quite possible that Aurora and Aphria could see nice gains once their stocks begin trading on the world's largest stock exchange. But which of these top Canadian marijuana stocks is more likely to enjoy a big bump from listing on the NYSE?

Why the NYSE listings matter

Does a listing on the NYSE really matter? Actually, yes.

U.S. investors can buy shares of Aphria and Aurora, but they have to do it through over-the-counter markets, often referred to as pink sheets. Some investors avoid buying pink sheet stocks. Why? Because these stocks don't have to comply with Securities and Exchange Commission (SEC) requirements, they're sometimes viewed as a little sketchy.

Listing on the NYSE accomplishes several things. First, it gives the marijuana stocks more legitimacy, at least in the eyes of some investors. Second, inclusion on the NYSE makes Aphria and Aurora more visible to U.S. investors. Third, it allows the stocks to be included in some mutual funds and exchange-traded funds (ETFs) that only hold positions in stocks traded on U.S. exchanges. And fourth, it dramatically increases the liquidity of the stocks.

There's no guarantee that these factors will cause the share prices of Aphria or Aurora to jump after listing on the NYSE. However, U.S. listings have helped other Canadian marijuana stocks this year. It seems likely that both Aphria and Aurora will experience an immediate benefit, as well.

The likely winner

So which of these two stocks is likely to receive a bigger boost? The smart money probably would be on Aurora.

For one thing, Aurora Cannabis already has attracted the attention of many U.S. investors thanks to speculation that Coca-Cola could be interested in a partnership. Yes, Coca-Cola had also reportedly been in talks with Aphria earlier, but it was Aurora that enjoyed the wave of recent publicity.

The exposure that the Coca-Cola reports gave Aurora to U.S. investors shouldn't be underestimated. Many major financial news outlets carried the story. Even though no deal has materialized yet -- and possibly never will -- the publicity helped make a lot of U.S. investors aware of Aurora Cannabis.

There's also the size factor. U.S. investors already are familiar with Canopy Growth and Tilray, both of which claim market caps of more than $10 billion. Aurora ranks third behind these two stocks, with a market cap of around $9.6 billion.

But there's an argument in favor of Aphria getting a larger bump from listing on the NYSE. The marijuana stock has flown under the radar for many U.S. investors. Aphria comes in a distant fourth place among Canadian marijuana stocks in terms of market cap. In some respects, Aphria has more to gain from increased visibility than Aurora does.

Timing also could help Aphria. Aurora's NYSE listing is coming hot on the heels of the opening of Canada's recreational marijuana market. Some investors appear to be taking profits off the table now that legalization is in effect. But Aphria isn't likely to trade on the NYSE for several more weeks. The passage of time could work to its benefit.

No easy street

While both Aphria and Aurora will soon have a presence on Wall Street, neither marijuana grower now has a stroll down Easy Street. It could take a few months for supply chains to stabilize with the launch of the Canadian recreational marijuana market. Product shortages have been reported across the country. Aphria CEO Vic Neufeld warned several days before the recreational market opened that if issues weren't resolved by January, "the whole program is in trouble."

That dire scenario probably won't become reality. However, Aphria and Aurora likely will face a serious problem within the next two or three years once supply surpasses demand. The resulting supply glut will no doubt cause tumultuous times for the Canadian cannabis industry.

Aphria, Aurora Cannabis, and some of their large peers are counting on the global medical marijuana market to absorb excess capacity. But there's no guarantee international markets will expand quickly enough to do so.

Still, the cannabis industry is here to stay. I think Aphria and Aurora will be, too. Billions of dollars will be made over the next several years in both recreational and medical marijuana. The companies with the credibility that U.S. stock exchange listings bring are likely to be among the long-term winners.