Salzburg's compact alpine airport doesn't accept widebody transatlantic service, which is precisely why every itinerary in business class from Nashville to Salzburg funnels through a major European or East Coast hub. There is no nonstop option from BNA, so the real decision isn't whether to connect, but where: Delta routes through Amsterdam or its JFK/Atlanta gateways before handing off to a partner for the short Central European hop, while United typically connects via Newark or Washington Dulles into Frankfurt or Munich, and Austrian Airlines—the natural specialist on this route—flies its own metal from a US gateway into Vienna before a quick regional jet down to Salzburg. Having flown all three configurations repeatedly, I'd steer discerning travelers toward routing through Munich or Vienna rather than Amsterdam or Frankfurt during winter, since Salzburg's small airport handles snow delays better when your final connection is short and operated by a carrier used to Alpine weather patterns.
Austrian's long-haul business class, flown on their 777 and 767 fleet, uses a comfortable lie-flat product with direct aisle access on the 777, and their Vienna hub offers one of Europe's more relaxed connection experiences, with a dedicated business lounge that's worth lingering in if you have a few hours before the Salzburg leg. Delta's transatlantic business cabins—Delta One suites on their A330-900s and 767s—offer full privacy doors on the newer aircraft, a meaningful upgrade if your routing puts you on that equipment through JFK or Amsterdam. United's Polaris seats, found on their 767 and 777 fleets serving Newark and Dulles, remain solid though slightly dated compared to Delta's newest cabins. My insider tip: book the earliest outbound connection you can find from BNA, because Austrian's Salzburg turboprop and regional jet connections operate more reliably in daylight hours, especially October through March when fog rolls through the Salzach valley.
Deal-wise, January through March and again in October and November consistently offer the softest business class fares on this corridor, as ski season demand hasn't yet peaked and Salzburg's summer festival crowds have cleared out. Given how erratically fares swing across three different routings and alliances, setting up automated fare alerts for this specific city pair is the smartest way to catch a premium seat before it disappears.