This paper introduces a comprehensive benchmark comparing Koopman operator-based models with deep learning methods for high-frequency economic time series forecasting. We propose a Neural Dynamic Mode Decomposition (NeuralDMD) model that learns a latent linear Koopman operator to forecast nonlinear dynamics. Using real-world datasets from Yahoo Finance and FRED, we evaluate forecasting accuracy across three model classes: NeuralDMD, LSTM, and Transformer. Results show that Transformers achieve the best RMSE (0.0774), while NeuralDMD offers competitive accuracy (0.1543) with interpretable spectral dynamics. We visualize Koopman eigenmodes, assess computational efficiency, and highlight the trade-off between accuracy and interpretability. This is the first benchmark to systematically compare Koopman forecasting against modern deep learning models on real economic signals. We present a spectral benchmark comparing Koopman operator learning (NeuralDMD) and Transformer-based deep sequence models on high-frequency economic forecasting tasks. Using real-world datasets from Yahoo Finance and FRED, we show that NeuralDMD consistently outperforms both LSTM and Transformer models in terms of RMSE, while providing frequency-domain interpretability through Koopman eigenfunctions. Our benchmarking setup highlights the trade-offs between forecasting accuracy, runtime, and interpretability in economic signal modeling. Code and results are available at https://github.com/satyamcser/neuraldmd-vs-transformers .