Tukey vs Duncan Post Hoc
Tukey's Honestly Significant Difference and Duncan's Multiple Range Test are both post-hoc procedures for ANOVA, but they control error rates differently. The choice between them is partly statistical and partly conventional. This page lays out both and gives a defensible recommendation.
What error rates each controls
Tukey HSD controls the family-wise error rate at alpha for all pairwise comparisons. The chance of even one false-positive across the entire family of pairwise tests is bounded by alpha. Duncan's Multiple Range Test does not control the family-wise rate; it uses a stepwise procedure with progressively wider critical values that controls a comparison-wise rate that is closer to alpha for adjacent means than for distant ones. As a result Duncan declares more significant differences than Tukey at the same nominal alpha.
Why agronomy still uses DMRT
Indian and historic agronomy literature (much of which traces back to Cochran and Cox) has used DMRT for decades, and many universities still require letter grouping in the DMRT style. The convention is so entrenched that paper templates from ICAR institutes and many Indian agricultural universities expect DMRT. Pragmatically, where the convention is required, use DMRT and report which procedure was used.
Tukey when you submit to international journals
Most international agronomy and biology journals now expect a family-wise-controlled procedure such as Tukey HSD or, where assumptions fail, Tukey-Kramer (unequal n) or Games-Howell (unequal variance). If you are unsure which is expected, run both and report the one preferred by your target journal; the underlying ANOVA decision is unchanged.