The Smithsonian’s National Portrait Gallery in Washington, D.C., holds the largest collection of presidential portraits in the country, stretching back to some very famous paintings of George Washington, whose birthday is today, Feb. 22. A small part of that collection makes up a popular ongoing exhibit at the gallery called “America’s Presidents.”

Last week, with much fanfare, the National Portrait Gallery unveiled the official portraits of Barack and Michelle Obama. From the outset, the buzz around these two works was significant and the event gave people plenty to talk about. Opinions pro and con piled up quickly, and rightly so: They’re well worth having an opinion about.

To paint his portrait, Barack Obama selected Kehinde Wiley, an American artist born in Los Angeles in 1977 who received his MFA in art from Yale in 2001. In 2013, GQ magazine called Wiley “one of the art world’s brightest lights,” and described his work as borrowing “heavily from the old to make something blazingly new.”

His primary style is to paint his subjects in formal, often heroic poses closely copied from earlier paintings of royalty (think Louis XIV of France or “Napoleon Crossing the Alps”) placed against an intensely colorful, patterned background. The busy background aggressively forces you to focus more deliberatively on the subject of the painting. Wiley is the first African-American to paint an official presidential portrait and his subjects are of African descent as well, usually an anonymous person he encountered on the street, but sometimes a celebrity.

Here, Mr. Obama is seated, leaning slightly forward in a simple wooden chair, arms crossed, elbows on his knees. The background is a riot of green foliage punctuated by bright flowers that represent elements of his life.

In contrast to Wiley, Amy Sherald, who painted Michelle Obama’s portrait, is less well-known. Or at least she was. She’s 44 and originally from Columbus, Georgia, now living in Baltimore. She received her MFA from the Maryland Institute College of Art in 2004 and had her first solo show in 2011.

Like Wiley, she is African-American and her portraits are focused likewise. But unlike Wiley, there is nothing formal or inflated in the way she renders her subjects. She has perfected a kind of grayscale palette for skin tones and allows the subject’s clothing to carry the weight of color in her paintings. People are usually posed standing straight up, facing the viewer squarely and without pretension. Backgrounds are monochromatic.

Ms. Obama is seated in a flowing, floor-length dress patterned in black and white segments, along with a few of red, pink and yellow. (Some have compared the dress to a Mondrian painting.) Her chin rests on the back of her hand. The composition is a classic triangular one, with her head at the apex of the triangle. The background is sky blue.

At first I preferred the portrait of Mr. Obama in large part because of the accuracy with which Wiley captured the former president’s likeness. But now, as I’ve looked at more of Sherald’s very impressive work beyond her portrait of the former First Lady, my preference might be changing.

Only time will tell if the artists’ styles age well, but they’re serious works that deserve serious attention, not the snide or sarcastic remarks one has occasionally heard in the past week.

Take a look for yourself, and if you’re in Washington, D.C., drop by the National Portrait Gallery. You will be glad you did, and you’ll make a new connection with the history of the country, of which we all could use a fresh view from time to time.