“Loud and Rich” could describe a significant demographic in the Hamptons, especially in the summer. But no: in this case, it is the title of a tour that features Loudon Wainwright III and Richard Thompson. The two veteran singer-songwriters will be making a stop at the Westhampton Beach Performing Arts Center on Saturday, October 10.

The Wainwright name is a familiar one in these parts. The patriarch of the clan, Stuyvesant Wainwright, represented the East End in the House of Representatives in the 1940s and ’50s and, at last report, is hale and hearty in his 90s in East Hampton. Last month, two of Loudon’s three children, Rufus and Martha, performed with Norah Jones in a benefit for the Watermill Center in Bridgehampton. When not on tour or recording, Loudon can be found on Shelter Island.

Putting him on tour with Mr. Thompson might at first appear to be an unusual choice. Mr. Wainwright was born in North Carolina and his career began in the folk-music clubs of Boston and New York in the 1960s. His first album was released in 1970 and he has always been a solo act, except when collaborating with family members. (He was once married to the Canadian singer Kate McGarrigle.) He has also been involved in acting, from playing Captain Calvin Spaulding (the “singing surgeon”) in the television version of “MASH” to supporting roles in such recent film fare as “The 40-Year-old Virgin” and “Knocked Up.”

Richard Thompson was born in the Notting Hill section of London—his father was a Scotland Yard detective—and in an interview he still sounds very much the English rocker, even though he has lived mostly in Los Angeles for the last decade. Arriving on the tail end of the British Invasion of the 1960s, he co-founded the band Fairport Convention in 1967 when he was only 18 and almost immediately was noticed by rock-and-roll critics for playing electric guitar.

He became a solo act in 1971 and wrote all of his own material. Mr. Thompson was back to being a collaborator when his wife, Linda, emerged as a singer and songwriter, and the album “Shoot Out the Lights” was a hit. The couple quit the business altogether in the mid-1970s to join a Sufi community in East Anglia, but were back recording in the studio within a few years. After his divorce in the ’80s, Mr. Thompson has been a solo act again, with his most recent album being “Sweet Warrior.”

So the two musicians have followed different paths, but Mr. Thompson doesn’t think that is a barrier to sharing the stage or an entire tour. “We just did Australia and Japan together, and it went very well,” he reported. “If you’ve been around for a while, you learn how to blend seamlessly with other musicians. I grew up listening also to folk music and I’m quite familiar with American traditional music. Plus I’ve known Loudon a long time and I’m familiar with his material, so it’s quite easy for me to jump up on stage with him.”

At 60 and with more than 40 years of songwriting on his resume, Mr. Thompson is at the stage of his career when two things are happening: a lot of musicians are covering his material, and he is trying to sort out career summaries from critics.

“Quite a few,” he responded to a question about if he likes cover versions of his songs by such artists as Bonnie Raitt, REM, Elvis Costello, Shawn Colvin, and even the Blind Boys of Alabama. “A songwriter writes a song and then it can sort of become other people’s property and has other lives. Sometimes you hear a version and go, ‘Ouch, that’s not good.’ On the whole, though, the covers I’ve heard have been pretty good.

“The most impressive kind of cover is the one that shows you as a writer something in the song that you hadn’t really seen there before. There have been times when another artist showed me the potential songs had that I hadn’t realized when I wrote them. I didn’t know they could be interpreted in that way.”

What can be difficult is when critics try to put the career of someone like Mr. Thompson in perspective, especially with comparisons. Last month, the Philadelphia Inquirer placed him in the same category as Neil Young and Prince as a songwriter and guitarist. Also last month, a critic in Rolling Stone wrote that he was “a perennial dark-horse contender for the title of Greatest Living Rock Guitarist.”

“It’s the first time I’m hearing most of this,” Mr. Thompson said. “I don’t go in pursuit of my own press clippings. Comparisons between musicians are usually a bit artificial. Ultimately, you can’t say one is better than another. It’s become a journalistic convenience rather than a true gauge of abilities and popularity. When musicians talk to each other, they never discuss such comparisons. We all bring something to the table.”