Let's get the basics out of the way first; Battle Royale II is as much of a sequel to Battle Royale as Predator 2 is to Predator. Meaning it takes place in the same world and have a similar theme, but that's about it. You won't be seeing any of the characters from the first part, and the story doesn't revolve around the program this time around. Instead, it's a different type of survival game, centered around teams.

Battle Royale II: Blitz Royale is not as horrible as some will lead you to believe.
In fact, it's a fairly good story, and every bit a spiritual successor of the original BR manga. They were both written by Koushun Takami, but with a different artist for BRII. Now the art of BRII is severely different from the one found in the first manga, and this apparently ruins the enjoyment for some people.
Most of the people who dislike the art are the typical "Naruto generation" that want their manga to have a certain sterile look and can't read anything that deviates from that formula. Others dislike the art because it's too different from the original manga. That's why you shouldn't go in expecting to read a straight up sequel, because you might find yourself turned-off when you find the art to be hugely different from the original manga. For those of you who aren't bothered by alternative looking manga, this is worth checking out.

Story:

The story of BRII may seem shallow at first glance, since the manga is rather short, but it does not disappoint. It's quite similar to BR but at the same time it's nothing like it. The psychological aspects and themes are there, and fans of the original story will most likely notice the similarities and find them well played out.

Art:

Now the art is what will break or make this manga for many. It's rather cartoony, and this will turn some people off, especially the aforementioned ones. The art might seem terrible at first, but is in fact rather effective as a sharp contrast to the violence and adult themes featured in the story.
If you've read any of Mohiro Kitoh's works, you won't have a problem though (other than the same problem found in Mohiro Kitoh's titles; character designs)

Characters:

Personally, I found the characters to be portrayed much better than the ones found in BR. It's centered around a select few rather then the whole class, for obvious reasons. You won't get to know them on a level as deep as the one in BR. However, the characters are realistic and believable, as compared to the sometimes hilariously unbelievable characters found in the original. As such, not exploring the backgrounds and mental disorders of the entire cast in BRII can be seen as a blessing in disguise, and makes the whole story feel more realistic. To voice some critizism towards the character designs, as previously mentioned, is that they are rather generic, and the only way to tell the characters apart is pretty much by looking at their hair.

Enjoyment:

As far as enjoyment goes, I found this manga to deliver.
There are few chapters, so it benefits from reading in one sitting, and since it's being short it never really loses it's momentum, and you will find yourself wondering what will happen next as the story progresses. It's short but handled well.

Overall:

A good read, albeit a little bit too short.
I for one wouldn't mind it to have been a little bit longer and the main characters could benefit from being explored a little deeper.
Still, it's a good short read that isn't for everybody, but nevertheless worth checking out.