As the oil rout continues to take its toll on the Canadian economy, the U.S. recovery remains on track. This is putting pressure on the Canadian dollar compared to its American counterpart, and the trend is likely to pick up steam when the United States begins to raise interest rates.

Bank of Montreal (TSX:BMO)(NYSE:BMO) and Toronto-Dominion Bank (TSX:TD)(NYSE:TD) both have significant U.S. operations. Let’s look at the two Canadian banks to see if one offers investors a better opportunity to profit from stronger U.S. growth and the increasing spread between the currencies.

Bank of Montreal

Bank of Montreal has been in the U.S. market since the early 1980s, when it purchased Chicago-based Harris Bankcorp. In 2011 it took advantage of an opportunity to double the size of the U.S. operation and bought Wisconsin-based Marshall & Ilsley Corp.

Today, Bank of Montreal has a strong presence in the U.S. Midwest, with 600 branches and three million clients. In a recent statement, CEO William Downe said he sees the U.S. customer base growing by 100% in the next five years.

In its Q1 2015 earnings statement, Bank of Montreal reported adjusted net income of $205 million from the U.S. operations. This was a 14% increase over the same period a year ago. Loan growth in the unit hit 10%, driven by strength in commercial lending. The U.S. division accounted for 20% of the company’s first-quarter earnings.

Bank of Montreal pays a dividend of $3.20 per share that yields about 4.2%.

Toronto-Dominion Bank

Toronto-Dominion Bank’s U.S. growth story is impressive. In the past 10 years the bank has gone from having almost no retail presence to being one of the top 10 U.S. banks. In fact, the company has spent nearly $17 billion to build a retail network that stretches from Maine right down the east coast to Florida.

With more than 1,300 U.S. branches, TD is taking advantage of the country’s economic recovery, as well as the strength of the U.S. dollar.

In Q1 2015, the U.S. retail operations delivered net income of US$536 million, a 16% year-over-year increase. When converted to Canadian currency, the results were $625 million, a 27% increase over Q1 2014. Loan growth in the U.S. was 9% and deposits increased by 5%. Based on the Q1 2015 total adjusted earnings of $2.1 billion, the U.S. retail operation delivered nearly 30% of TD’s profits.

Toronto-Dominion pays a dividend of $2.04 per share that yields about 3.75%. The company recently increased the payout by 9%.

Which should you buy?

Both banks are trading at reasonable valuations and will continue to benefit from improving economic conditions south of the border. At this point, Toronto-Dominion is probably a better pick based on the size of its U.S. operation.

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Fool contributor Andrew Walker has no position in any stocks mentioned.