Before we start....

Please note that the rest of this review contains spoilers for 20th Century Boys. This review is written assuming that you've read it, as 21st Century Boys is a direct continuation and acts as an epilogue. There are no major spoilers for 21st Century Boys in this review. If you are here and wondering if it is worthwhile to read, my review of 20th Century Boys goes a bit more in-depth, but the short answer is yes if you like sci-fi and mystery. I've you've already read it and want to know if 21st Century Boys is worth reading, the short answer is also yes. Most of my thoughts about 20th Century Boys applies here.
Because the manga is only two volumes this review won't be structured like usual.

#What I Liked
It gave much needed closure to characters like Manjoume and Sadakiyo. The highlight of the epilogue for me was definitely Kenji's exploration of the virtual attraction. Seeing him try to make amends and confront the second friend in his childhood were all memorable and interesting moments which reminded me of how good Naoki Urasawa is at character writing. All of the characters are as interesting as they were before and there appearances here felt like a more proper conclusion. As always, the art is fantastic and comparing it to the start of Monster or 20th Century Boys shows Urasawa's growth and improvement over the years.

#What I Didn't Like as Much
I wish that it was only character closure. Another world-ending scheme from Friend is introduced here, in the form of an anti-proton-bomb. It may have made sense to include given that the 20th and 21st Century Boys were written several years apart, but after reading them back to back it only feels unnecessary.

There was also a plot twist at the ending, which is only included in the Perfect Edition, which made me extremely confused. It is explored more in this thread (CONTAINS SPOILERS). I felt like Urasawa was trying to replicate the success of one of his other endings and the discussion that surrounds it. Mentioning what it's from would spoil the other series as well. I am also not satisfied with what happened to the character of Professor Shikishima's daughter. It seemed like it came out of nowhere. It also contains some cliché aspects similarly to 20th Century Boys' final act.

Conclusion

It was enjoyable and it cleared up the cliffhanger ending of 20th Century Boys, and provided some great character moments, but it could have been condensed to just this closure. The end-of-the-world subplot appearing another time had no stakes and felt unnecessary, but it doesn't detract too much from the conclusion to this fantastic series.