Traditional particle-based simulations struggle with large bottlebrush copolymers, consisting of many side chains grafted to a backbone. Field-theoretical simulations (FTS) allow us to overcome the computational demands in order to calculate their equilibrium behavior. We consider bottlebrushes where all grafts are symmetric diblock copolymers, focusing on the order-disorder transition (ODT) and the size of ordered domains. Increasing the number of grafts and decreasing the spacing between them both raise the transition temperature. The ODT and lamellar period asymptotically approach constants as the number of grafts increases. As the spacing between grafts becomes large, the bottlebrushes behave like diblock copolymers, and as it becomes small, they behave like starblock copolymers. In between, the period increases, reaching a maximum when the spacing is approximately 0.35 times the length of the grafts. A comparison of FTS with mean-field calculations allows us to assess the effect of compositional fluctuations. Fluctuations suppress ordering, while having little effect on the period, as is the case for diblock copolymers.