AI research agents accelerate ML research by automating hypothesis generation, experimentation, and empirical refinement. Existing agent strategies range from greedy hill-climbing to tree search and evolutionary optimization, yet which strategy choices drive performance remains unclear. Answering this question requires a benchmark that separates agent strategy (e.g., search topology) from execution infrastructure (e.g., code editor), so that performance differences are attributable to strategy rather than infrastructure, and that provides process-level metrics beyond final scores to analyze exploration behaviors. Existing benchmarks offer limited support. We propose FML-Bench, a benchmark of 18 fundamental ML research tasks across 10 domains that separates agent strategy from execution infrastructure and defines 12 process-level behavioral metrics. Evaluating six representative agents, we find that: (1) strategy complexity alone does not guarantee strong performance: a simple greedy hill-climber nearly matches the best-performing tree-search agent, both well above the remaining agents; (2) our analysis suggests this pattern relates to improvement opportunity structure: greedy search tends to be more effective when opportunities are dense, while tree-search and evolutionary strategies tend to be more effective when opportunities are sparse; an adaptive agent built on this insight switches to broader exploration upon detecting improvement stagnation and outperforms the other six agents, lending initial support to this observation; and (3) process-level analysis reveals that early convergence and directionally focused exploration are significantly associated with final performance, while solution diversity and compute cost are not. Our benchmark is available at: https://github.com/qrzou/FML-bench.