The advent of the Transformer has led to the development of large language models (LLM), which appear to demonstrate human-like capabilities. To assess the generality of this class of models and a variety of other base neural network architectures to multimodal domains, we evaluated and compared their capacity for multimodal generalization. We introduce a multimodal question-answer benchmark to evaluate three specific types of out-of-distribution (OOD) generalization performance: distractor generalization (generalization in the presence of distractors), systematic compositional generalization (generalization to new task permutations), and productive compositional generalization (generalization to more complex tasks with deeper dependencies). While we found that most architectures faired poorly on most forms of generalization (e.g., RNNs and standard Transformers), models that leveraged cross-attention mechanisms between input domains, such as the Perceiver, fared better. Our positive results demonstrate that for multimodal distractor and systematic generalization, cross-attention is an important mechanism to integrate multiple sources of information. On the other hand, all architectures failed in productive generalization, suggesting fundamental limitations of existing architectures for specific types of multimodal OOD generalization. These results demonstrate the strengths and limitations of specific architectural components underlying modern neural models for multimodal reasoning. Finally, we provide Generic COG (gCOG), a configurable benchmark with several multimodal generalization splits, for future studies to explore.