I agree with people's suggestion of deciding based on the length of the flight, but want to mention some additional criteria: segment, direction, arrival time and crowding.
Though most airline and third-party booking sites don't make this obvious, not all of the flights in your itinerary have to be business class. You can price mixed-class itineraries using Google's ITA Software site (Advanced controls, Extension codes, Faring, +CABIN) and you can coax some Web sites to book them. Otherwise, call the airline.
To me, it's worth paying extra to arrive in Europe well-rested. If my arrival time is early in the day, as is typical for US–Europe flights, I will pay for business class in that direction. For the return direction, I don't care as much, because I won't be missing out on anything if I need to rest for a day or two at home.
If my itinerary includes a connection on the way to Europe, I might opt for business class on the domestic segment if connection time is short and there are few alternative flights to Europe. Being first off the plane reduces the odds that I'll be stuck in an airport hotel for the night.
If the airline has a decent international premium economy offering, I might even chose business for the domestic segment and premium economy for the transatlantic segment. We can grumble about transatlantic coach, but domestic coach is guaranteed to be worse!
Last but not least, if I'm traveling during a busy season, on a busy day of the week, or at a busy time of day, I'm more likely to choose business class for the affected segments, just to avoid waiting in lines and dealing with crowds.
There are many ways to save money on business class. (All bets about fares are off after the shock of the pandemic, though.)
First, you might find a discounted business class fare on a single segment, that you wouldn't qualify for if you chose business class for the whole itinerary — because the discounted business class fare might be sold out on the other segments, kicking the whole itinerary up to a higher business class fare.
Second, connections and airline alliances
can help. If business class is expensive on a direct flight, consider connecting. If one airline charges a high business class fare, see if a codeshare partner can sell you a ticket on the same flight, at a lower price.
Third, more and more airlines are offering paid upgrades. Sometimes you can buy at a known price, either long before you fly, a few days before you fly, or during the check-in window. Some airlines let you submit a bid, and give you an answer a few days before you fly. Paid upgrades are not always advantageous, but they are worth looking into.