Byteball is an interesting one. Full disclosure: I have not participated in any of the events to receive Byteball from my BTC holdings. Byteball is a Russian product if that means anything to you.

Byteball is not a blockchain - that is their somewhat innovative feature. They use something called a DAG which is a type of acyclic data-structure that is basically like an infinite branching tree. Without diving into the specifics of this, (frankly Wikipedia will do a better job outlining what a DAG is) this allows a form of transaction finality almost immediately. DAGs have many tradeoffs compared to blockchains - expecially when it comes to growth of the chain/database. DAGs can 'become to thinly spread' a problem inherent to the data structure. This structure does remove some of the scaling limitations inherent to blockchain databases.
The DAG also removes concepts like confirmations and types of probabilistic finality come to play.

From my understanding (I have not read the entire 49 page white paper - way too long imo) Byteball uses a sort of DPOS consensus protocol where there are validating nodes whom are elected by the network.

They have a clean-looking app and chat-bot setup going for them. Could be useful. They have added smart contracts and this form of "conditional payments" to their network which add functionality. There is little decentralization in the teams working on the project so this can be a problem going forward. I am not sure how well all their applications will catch on. Only time can tell.

Their dark send anonymity features do not seem very innovative to me and due to their strictly peer-to-peer nature, they seem inherently insecure; or inherently less secure than other methods. We will have to see how it plays out in practice and in competition with strictly fungible coins like Monero and Zcash.

It is probably clear from this post that I am not entirely sold on the idea of Byteball. I don't see the need to make the tradeoffs required by DAG structures. I am personally not a fan of the Bitcoin mirror release. It seems less scammy - no ICO and all but I believe there are some problems with this schema.

Overall, if you can get some free Byteball with your BTC, go for it! I don't know if I would be hanging on to Bytes for too long though.