Chip designers Advanced Micro Devices (NASDAQ:AMD) and NVIDIA (NASDAQ:NVDA) have been crossing proverbial swords for decades. They form a nearly unchallenged duopoly in the market for computer graphics processors, and the same chips can also churn through other types of advanced math problems at impressive speeds.

The two companies may look almost identical to a casual observer, but AMD and NVIDIA stand worlds apart when seen through a seasoned investor's lens. Let's take a look at the key differences between these companies, and then I'll show you which one you should buy today.

By the numbers

NVIDIA is a much larger business than AMD at the moment, and it's been nearly a decade since AMD could match NVIDIA's profit margins:

NVDA Revenue (TTM) Chart

NVDA Revenue (TTM) data by YCharts

That combination leaves NVIDIA dwarfing AMD in terms of free cash flows and bottom-line profits:

NVDA Free Cash Flow Chart

NVDA Free Cash Flow data by YCharts

Rocket fuel

NVIDIA's sales growth stems from success in the data center. The company's data center sales increased by 80% year over year in last week's first-quarter 2021 report. This market accounted for 37% of NVIDIA's total revenues in the first quarter, up from 29% in the year-ago period and a mere 8% two years ago. NVIDIA's data center ambitions are paying dividends and will accelerate in the coming quarters as the $6.9 billion buyout of data center networking specialist Mellanox starts to bear fruit.

Most of AMD's revenue growth for the same reporting period came chiefly from desktop and notebook processors. AMD gets to double-dip in these markets as a major provider of both Ryzen system processors and Radeon graphics chips. Notebook sales spiked due to work-at-home orders under the COVID-19 health crisis. Looking ahead, AMD expects semi-custom chip sales to sure in the second half as both Sony (NYSE:SNE) and Microsoft (NASDAQ:MSFT) are launching new gaming consoles built around AMD's products.

Two hands giving thumbs-up and thumbs-down signs in front on several uncut wafers of silicon chips.

Image source: Getty Images.

Which stock should you buy today?

Both of these stocks have held up very well during the coronavirus pandemic. AMD's shares have gained 16% year-to-date while NVIDIA's stock price increased by 48% and both have more than doubled over the last year. Investors clearly expect the good times to keep rolling.

As a result, we're looking at some nosebleed valuation ratios here. AMD is trading at 130 times trailing earnings and 144 times free cash flows. NVIDIA's values for the same ratios stand at 77 and 52, respectively.

In order to justify these sky-high valuations, both NVIDIA and AMD need to present fantastic revenue and earnings growth for several years. I'm not betting against either one of these high-growth dynamos as they stare down some massive growth opportunities in the near term. In the long run, AMD will need to pick up its data center game while NVIDIA can simply continue to execute on the same ideas that brought the company this far.

Therefore, I'd rather buy NVIDIA today at slightly more reasonable share prices and a clearer path toward continued success.