Earlier this year, we pitted payments processing companies American Express (AXP -0.08%) and Square (SQ -1.97%) against each other. At that time, I unequivocally picked the former as the superior stock investment.

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Since then, the fortunes of the two companies have diverged somewhat. American Express' most recently reported quarter exacerbated lingering concerns about the loss of its Costco (COST -0.55%) business. Meanwhile, potential usurper Square beat convincingly on both the top and bottom lines in its latest frame.

So it's a good time to revisit the question previously asked: Which of the two stocks is the more appealing buy just now?

It's hip to be...

Square posted big improvements in many crucial areas in its just-reported Q2. 

There were the revenue and earnings beats, of course. Square's $439 million in quarterly net revenue and $27 million, or $0.08 per share, loss were better than analysts projected. 

But the company also saw an impressive 54% revenue gain when its proceeds from a soon-to-expire payments processing deal with Starbucks are stripped out, and overall gross payment volume saw a 42% rise. 

And the proportion of its sales have shifted dramatically in favor of larger businesses, a good sign that it is being taken more seriously by heavy hitters.

Meanwhile, scrappy Square has also done a good job of boosting the take from auxiliary products and services; hardware (i.e., credit card reader) sales zoomed over 200% higher to $11 million. Additionally, new product launches improved sales from software and services, by 130% to $30 million.

The better-than-expected results have given life to Square's stock price, which had been dragging in the wake of the company's IPO last November. Over the past week, the shares have risen by 10%, well in excess of American Express' 3% gain.

Leaving home without it

Some Square investors might feel the loss of Starbucks is a blow, but that won't hurt anywhere near as much as American Express' divorce from Costco. To recap that sad story, in Feb. 2015 the retailer dropped AmEx as the exclusive credit card accepted at its stores, as well as the co-branding partner of its own cards.

To say that this affects AmEx's business is an understatement, as roughly one out of every ten AmEx cards in circulation was Costco co-branded plastic. The divorce was long, with the transition to the new Costco partners -- Citigroup as the issuer and Visa as the card brand -- only being completed this past June. 

AmEx's Q2 was when the hand-off occurred. For the quarter, the company's net profit topped $2 billion, compared to the Q2 2015 result of $1.5 billion.

The quarter's results, however, were inflated by a one-time gain from the mandated sale of the Costco portfolio to Citigroup, amounting to $677 million after taxes (although this was offset by a $151 million restructuring charge).

Revenue, meanwhile, declined marginally on a year-over-year basis to $8.2 billion and came in under analyst estimates. This is a big concern to investors and it should be; on a trailing 12-month basis, it's been dropping since just before the Costco split.

A proven moneymaker

So, of the two, Square is the company favored by investors now.

But it isn't the one I'd pick. Yes, that most recent quarter was impressive, and the company's business seems to be moving in all the right directions.

One quarter, however, does not an investment case make. And we should keep firmly in mind that in spite of impressive revenue gains, Square remains unprofitable on the bottom line.

Meanwhile, there are a host of 21st century payment solutions rivaling the company's, and competition will be very hot. Square hasn't yet sufficiently proven that it can thrive in the heat.

AmEx, in my opinion, has demonstrated that it can compete and do so effectively. Even taking the Costco breakup into consideration it's still an extremely profitable enterprise. And that's hardly the first setback in its long history.

AmEx is a survivor and thriver because, over the years, it's built something of a moat -- it's arguably the only card brand that has real cachet. An AmEx card is a status symbol, in a way that Visa, MasterCard, and their ilk are not. AmEx's customer base is relatively affluent, and it tends to be loyal.

So despite the recent divergence in fortunes, I remain an AmEx bull and I favor it over Square. The credit card incumbent still has a good position in the market, and is a proven moneymaker -- even when it suffers a body blow like the Costco abandonment.

Although it might take some time, I feel strongly that AmEx will recover from the hit. And before long, it'll get back into the market's good graces.