For decades, Canadian Imperial Bank of Commerce (TSX:CM)(NYSE:CM) has frustrated its shareholders. Most recently, the bank got caught up badly in the U.S. sub-prime mortgage market, leading to over US$10 billion in write-downs. Before that, CIBC had to pay a $2.4 billion settlement in the wake of the Enron fiasco. The bank also suffered losses from the East Asian financial crisis. And the list goes on.

Meanwhile, Royal Bank of Canada (TSX:RY)(NYSE:RY) has been somewhat of a model citizen. The bank’s growth strategy has mostly been disciplined. It prudently exited the money-losing U.S. retail business. It suffered only modestly during the financial crisis.

Tellingly, a $10,000 investment in RBC 15 years ago would be worth over $50,000 today. If that money was put into CIBC shares, it would be worth less than $32,000.

That being the case, now is actually a wonderful time to buy CIBC over RBC. Below we take a look at three reasons why.

1. A renewed sense of discipline

Five years ago no one predicted that CIBC could become more disciplined than RBC. Yet that’s exactly what has happened.

To illustrate, CIBC has been looking to grow its wealth management business in the United States, but has shown it won’t overpay for acquisitions. In fact, the bank hasn’t made any wealth management acquisitions since the US$210 million purchase of Atlantic Trust in late 2013. CIBC was in the running to buy Russell Investments last year, but ultimately lost a bidding war to the London Stock Exchange.

Meanwhile, RBC has opened its wallet in a big way, paying$5.4 billion for City National, a private bank from California known for its high-profile clientele. RBC paid roughly 2.6 times tangible book value, prompting one analyst to call the purchase “the most expensive large U.S.-bank deal announced since the financial crisis of 2007 and 2008.”

Clearly, CIBC is worried about not repeating past mistakes, and one has to wonder if RBC has gotten cocky.

2. A better-capitalized bank

CIBC is commonly referred to as a risky bank, but it’s better capitalized than RBC.

To illustrate, CIBC has a common equity tier 1 ratio of 10.8%, while RBC’s stands at only 10%. Thus, CIBC has plenty of cash to spare, which could easily be used to buy back shares or pay a bigger dividend.

3. A better price

CIBC is better capitalized and seems to have more discipline than RBC. But RBC is the more expensive stock, trading at 12.2 times earnings and 2.2 times book value. Those numbers are only 10.6 and 2.0 at CIBC. Consequently, CIBC has a healthy 4.5% dividend yield, easily surpassing RBC’s 4.0%.

It seems that CIBC’s past misdeeds are still affecting the bank’s reputation, even though the bank has completely transformed itself. As a result, its shares remain depressed. So, if you’re looking for a nice bargain, you’re much better off with CIBC than RBC.

What about the other banks?

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Fool contributor Benjamin Sinclair has no position in any stocks mentioned.