Hash Rush looks cool!, Thank you for the link. Comparing Steemmonsters and Axie is like comparing apples and oranges, really. These are both games and they both run on the blockchain, but apart from that from that there is not much to compare. For example: a Steemmonster card like Malric Inferno has it stats and those basically stay the same, only getting higher with the lvl of the card. But the other players have the same Malric Inferno card. With the same stats on the same lvl.
If I take an axie on the other hand, Every Axie has different stats and parts, which gives them different attacks and possibilities. No other player can have the same axie as me.
It seems with next gen game, we mean exactly the same: actual games instead of collectibles. HashRush seems to be another genre though.