All three are large mixture-of-experts models, but they optimize for different things. DeepSeek R1 is a 671B MoE from January 2025, trained explicitly for chain-of-thought reasoning. AIME and MATH benchmark performance is in the range of frontier proprietary models. The 128K context window handles long problem contexts well. The DeepSeek license permits commercial use with conditions, and the model is available through DeepInfra, Fireworks, and DeepSeek's own API. It is the right default when explicit reasoning traces, mathematical reliability, or step-by-step problem-solving quality are the primary evaluation criteria. DeepSeek V3.2 is the general-purpose sibling, released May 2025 with the same 671B total / 37B active architecture but optimized for broader task coverage — code generation, instruction following, summarization, and chat quality — rather than explicit reasoning depth. The May 2025 pricing drop made it approximately 30 percent cheaper than V3. If your workload does not specifically require reasoning chain visibility and you want the best cost-adjusted general quality available in open weights, V3.2 is the stronger choice over R1. Mixtral 8x22B Instruct is Mistral's April 2024 MoE, 141B total parameters with 39B active per pass and a 64K context window under Apache 2.0. It is nearly two generations behind the DeepSeek releases on benchmark quality, but Apache 2.0 is still the cleanest license in this comparison for commercial deployment and redistribution without legal overhead. Teams that need full self-hosting rights and cannot accept non-Apache terms will find this the only suitable option here. Pick DeepSeek R1 for reasoning-heavy pipelines where chain-of-thought quality is measured. Pick DeepSeek V3.2 for general-purpose workloads where cost-adjusted quality is the priority and licensing is manageable. Pick Mixtral 8x22B when Apache 2.0 freedom and stable, audited open-weights infrastructure matter more than raw benchmark scores.