TLDR: watch whichever you feel like watching.  

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You can actually watch it in any order. Having seen both of them, except for the same protagonist they don't have any link between them. 

*Handa-kun* is an anime in which the protagonist is a high school student. This one leans highly towards comedy than a slice of life. But it's definitely fun to watch.

*Barakamon* is more the typical slice of life anime with bits and pieces of comedy, it has a sense of purpose unlike *Handa-kun* which is just everyday events. Here *Handa-kun* is grown-up and is trying to find some inspiration.