This technical analysis evaluates the trade-offs between classical NLP methods and Large Language Models (LLMs) by assessing four primary variables: document volume, output space (closed vs. open), label availability, and constraint profiles (latency, determinism, and auditability). For tasks with closed output spaces, such as fixed-taxonomy classification or standard entity recognition, classical methods like linear models or local NER pipelines are significantly more efficient. The author provides a mathematical framework to determine the break-even volume (V) for transitioning from hosted models to local systems, using the formula V > (F/T + m) / c, where F is the one-off development and labeling cost, T is the amortization horizon, m is monthly maintenance, and c is the per-document hosted cost. In a worked example assuming a $0.20 per million token price, a $13,200 development cost, and a 24-month horizon, the break-even point is 10 million documents per month. However, for open output spaces like summarization or multi-step reasoning, LLMs remain the only viable option. The article concludes that the most effective architectures are "cascades," where cheap, deterministic methods like regex or BM25 handle the bulk of the workload, escalating only ambiguous cases to more expensive models to optimize cost and performance.