Pan Am in the early 1960s had equally-sized fleets of DC8s and 707s, until they sold off the DC8s in the late 1960s and replaced them with more 707s. Unfortunately all their timetables of the period just state 707/DC8 for everything so not apparent which type was used for their longstanding PA1/2 round-the-world flights. Due to the need to slip crews along the way they presumably kept to one type. Certainly through London in the 1960s they seem to have used half-and-half of each type.
I don't think the 8s ever were used on the PanAm RTW (Round the World) flights (which actually were not quite round the world because PanAm did not have US domestic rights then so PA1 was LAX-JFK and PA2 was JFK-LAX - both the
very long way!). The same aircraft did not always go the whole way with maintenance issues, etc, so it is possible that 8s were substituted now and again on the LHR-JFK legs, etc. Pretty sure there was a period in the early 70s when 747s operated daily JFK-LHR-JFK and 707s the rest of the way - or at least to the Far East (probably TYO) where, I think, 74s took over again for the Pacific hop.
My personal DC-8 experiences were a bit eclectic - in 1970 Frankfurt - Heathrow in a Delta DC-8-30 operating a PanAm flight, 1971 Oslo (FBU) - Copenhagen in an SAS DC-8-63 (last very short hop of a long haul flight - from LAX I think - seemed a waste of such a beast - the interior was like looking along a very long tunnel - most unusual), 1972 Marseilles - Le Bourget in a UTA DC-8-62 (final leg of a UTA African flight) and,
best of all, in 1972 JFK - LAX in a United DC-8-21 (which had been converted from an -11 so was a very early machine and nearing the end of its mainline days).
The UA flight was exceptionally pleasant as it was in First Class and FREE (I won the flight as a prize!).
Nice planes to fly in (rather 'grand' and spacious) but the -63 just didn't 'feel' right to me - just a bit too stretched.