Negative reviews seem to centre around the argument that Handa-kun wasn't worthy as a predecessor to such a well-reviewed anime, and despite having some returning characters, doesn't actually share much in theme with Barakamon, disappointing hardcore fans. Handa-kun's comedy is quite different to Barakamon's and is far more comparable as a series to Danshi Koukousei no Nichijou or Sakamoto desu ga?, than it is to the anime it is supposed to set the stage for. I can understand some disappointment, if you were hoping for more Barakamon content, but it really was quite clear from the start of episode 1 that this show wasn't really attempting that, at that point one ought to shift their expectations for the content rather than rile oneself up over the differences between the two anime. I think it's unfair to blast the series with a '2' or a '3' simply because you're annoyed that you might have to wait a while longer for an actual continuation of Barakamon's story. It's not worthy of a '10' or '9' either in my opinion, but I think that's just an attempt by some to boost the score to offset the overly-negative reviews, which is not what the scoring system is for.
In my opinion, Handa-kun is a fun and refreshing comedy, undeserving of the hatred it receives from some Barakamon fans. In a way, it isn't really a prequel at all, Handa goes through very little character development until the final episode, and it doesn't really tell us anything relevant to the story of Barakamon. You really could question why the series even bothers to use the same characters. Despite being a different type of show to Barakamon, it doesn't negatively impact on its sequel either. The characters, while not revolutionary or multidimensional, are entertaining and give the whole anime a carefree, relaxed vibe making it easy and pleasant to watch. The whole show is very easy on the eye and ear, the characters, the palette and the soundtrack all contribute to making the show something you can enjoy casually watching, not demanding your full concentration. It certainly had me refreshing my browser waiting for the next episode to come out.
TL;DR - If you haven't watched Barakamon, watch them both, the order doesn't matter, they're both good albeit in different ways. If you have watched Barakamon and DON'T feel a primal urge to protect the thematic integrity of its universe and lampoon anything which taints your holy anime, then watch Handa-kun, you'll have fun, it's not as good as Barakamon, but that doesn't mean it's an insult either.
