What is the biological basis for tiredness after eating?
High carbohydrate meals will undoubtedly increase the relative levels of insulin, increase the shuttling of glucose from the blood to the cells, and leave you fatigued in wake of that. See reactive hypoglycemia. Reducing carbohydrate consumption should, to some level, reduce this effect. Caffeine should just as likely increase blood glucose levels by increasing glycogenolysis through PKA activation.

As Chris Stronks pointed out, eating can cause low blood pressure via redistribution of blood.