Vision-Language-Action (VLA) models have rapidly converged on a small set of architectural patterns: discrete-token autoregression (e.g. OpenVLA) and continuous-action flow-matching (e.g. pi-0.5). Yet preference alignment via Direct Preference Optimisation (DPO) -- the de-facto post-training step in language models -- has been studied almost exclusively on autoregressive VLAs. We present CrossVLA, an empirical study of cross-paradigm VLA post-training. Three contributions: (i) a surrogate flow-matching log-probability estimator that lets DPO operate on continuous-action backbones without probability-flow ODE integration; (ii) a head-to-head comparison of LoRA and DoRA as the parameter-efficient layer for VLA DPO, finding DoRA improves over OpenVLA SFT by a mean +10.4 pp across LIBERO 4-suite (600 trials, 3 seeds) -- per-suite +20.0 Object, +11.0 Long-horizon, +8.0 Goal, +2.7 Spatial -- with zero seed variance on Object (38/50 on each of 3 seeds); (iii) an inference-time anatomy showing the denoise loop dominates 78.6% of sample_actions latency and prefix-K/V caching a la VLA-Cache caps at a 21% acceleration ceiling -- both chunk-level and token-level cache strategies degrade success rate to 0-80% in our benchmarks. We further pretrain a multi-view + temporal projection head on 6000 LIBERO frames, achieving 99.5% k-NN recall@1 for same-task retrieval (36x over random), available as a downstream initialisation. All code, ckpts, training logs, and reproduction scripts are open at https://github.com/lz-googlefycy/vla-lab.