When it comes to investing in bank stocks, there are a lot of different types of institutions to choose from -- large or small, local, regional, or national, and recently, brick-and-mortar or internet-based. With that in mind, let's look at these two high-potential but extremely different bank stocks to see which might be the better addition to your portfolio right now.

Two different kinds of banks

Of the two banks being compared, I think it's safe to assume that most people are far more familiar with Bank of America (NYSE:BAC). The bank serves about 47 million customers through its network of 4,700 branches and 16,000 ATMs, and has about $2.2 trillion in total assets. While it has emerged as a leader in banking technologies such as mobile deposits and a state-of-the-art online banking platform, Bank of America as a whole is more of a traditional bank than BofI.

Door to a building with "bank" engraved on top.

Image source: Getty Images.

The bank offers a wide variety of products and services. In addition to consumer banking services such as checking/savings accounts, mortgages, credit cards, and auto loans, Bank of America also has a thriving global wealth and investment management division, corporate banking, trading business, and more.

On the other hand, BofI Holding (NYSE:AX) is a much smaller institution, with about $8 billion in assets -- not even half of 1% of Bank of America's size by this metric. However, from an investor's standpoint, this means that the bank has more room to grow.

Unlike Bank of America, BofI (which stands for "Bank of Internet") doesn't have any physical branches at all -- its operations are entirely online. Also unlike Bank of America and its assortment of businesses, BofI's business more closely resembles a typical savings and loan. The bank takes in deposits (mostly savings or checking) and loans money to consumers and small businesses.

It's important to point out that I'm a big fan of both banks as long-term investments. Here's a recent article I wrote about Bank of America's potential, and another one about BofI being a potential "millionaire-maker" stock. However, the reasons I think each bank could deliver great returns are quite different, and that's what I'd like to focus on here.

Bank of America is still rather cheap, but there's a reason

If you follow Bank of America closely, you may be thinking: "How can he call it cheap? The stock price has doubled over the past year!"

That's true, and Bank of America certainly isn't as cheap as it was. However, the bank's book value (the net value of all the bank's assets) is $24.04 per share, which means that as I write this, Bank of America trades for just 6% above its book value -- a rather low valuation compared with most peers.

BAC Price to Book Value Chart

BAC Price to Book Value data by YCharts.

However, there is a good reason for the low valuation. Bank of America has not been able to generate what most bank investors would consider a good level of profitability. Banks typically need to generate a return on equity (ROE) of 10% to cover their cost of capital, and a 1% return on assets (ROA) is also an industry benchmark. Bank of America's most recent numbers of 7% and 0.85%, respectively, aren't quite up to par.

However, as I discussed in the article I linked to earlier, I feel there is good reason to believe this will change in the near future, especially if interest rates continue to rise as expected.

In a nutshell, when you invest in Bank of America today, you're betting on the bank's ability to increase its profitability to a respectable level and keep it there. If this happens, shareholders could be handsomely rewarded.

BofI is highly efficient and profitable, but you'll pay the price for it

Unlike Bank of America, BofI's branch-free business model has given it the cost advantages it needs to be highly efficient and profitable. BofI's 2016 ROE of 19.4% and its ROA of 1.75% are far better than the industry benchmarks. So, the fact that BofI trades for nearly three times its book value may seem excessive at first, but the ability to generate roughly twice the profitability as the banking industry benchmarks call for helps justify the lofty valuation.

Further making the case for paying BofI's high price of admission is the bank's rapid pace of growth in recent years. Deposits grew by 27% and assets grew by 23% in the past year alone, and the bank's earnings per share (EPS) has grown at an annualized 32% rate since 2011, which continuously improving the bank's return on equity. As a result of the fast growth, book value has more than tripled over the past six years.

Chart of BofI's EPS and ROE growth since 2011.

Image source: BofI investor presentation.

To sum it up, by investing in BofI today, you're betting that the rapid growth rate will continue, and that we're still in the early innings of the company's expansion. If this proves to be the case, there's no telling at how well shareholders could do.

Which is the better option?

To be clear, both of these banks look like attractive options right now, especially with Donald Trump in the White House and a Republican majority in Congress. BofI has already proven its ability to run an efficient and profitable banking operation, and has lots of room for growth. Bank of America, on the other hand, trades cheaply and while its long-term growth potential is much more limited than BofI's, investors could certainly do quite well if the bank's profitability grows to a respectable level over the next few years.

Personally, I'm more of a Bank of America fan right now, as I believe rising interest rates and looser regulations will benefit it more than most other banks. However, I don't think you can go wrong with either option.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.