Both have a place, and most engagements end up hybrid. Cloud-hosted models (OpenAI, Anthropic, Bedrock, Azure AI) give you the latest frontier capabilities with minimal ops overhead — pay-per-use, scale up instantly, no model-serving infrastructure to maintain. On-premise or private-cloud models (self-hosted Llama, Mistral, Qwen, and similar) give you full data control, predictable costs, and air-gapped deployment when regulations require it — but you take on the serving, scaling, and updating work. We typically map the decision against four factors: data sensitivity, latency requirements, scale, and your team’s MLOps capacity. For regulated industries, a common pattern is a cloud frontier model for general tasks plus self-hosted smaller models for sensitive data flows.