Packet switching and circuit switching are the two main ways to operate all-optical networks in datacenters (DCs). Although optical circuit switching (OCS) is not a good fit for all scenarios, it is often considered appropriate for managing large flows. On the other hand, options based on packet switching, such as optical packet switching (OPS) or optical burst switching (OBS), are considered suitable mainly for small flows at best due to their lack of random-access buffers to manage packet contention. We accordingly study the throughput that applications can achieve in an all-optical DC network composed of fast all-optical switches, where large flows are managed by OCS and the rest by bufferless OPS. We focus on representative DC networks such as fat-trees, hypercubes, and rings, and take into account empirical application workloads, transport protocols, lack of RAM or fiber delay lines for buffering purposes in OPS switches, and characteristics of the network control plane. Surprisingly, we have found no scenario that requires OCS instead of OPS in order to increase application throughput; this holds even when all flows have unrealistically large sizes of tens of GB or larger. Counterintuitively, bufferless OPS offers much higher throughputs than OCS when managing large flows, and the lack of buffers in the OPS switches is irrelevant in this respect.