Both anime have eccentric characters, although people may not agree with me about that concerning New Game!!. Both casts get along surprisingly well despite their obvious personality differences and conflicts. The comedy tends to be a bit over the top. Both opening theme songs are amazing fun songs that introduce the viewer to the type of environment the shows offers. Both shows are in the slice of life and comedy genres. Every episode builds up the overall simple story, in both shows, but they seem episodic to an extent as well, so accidentally watching one episode out of order (not that I did) shouldn't throw off your understanding of what's happening.
I may be recommending the second season of New Game!, New Game!!, but both seasons are worth watching. Someone already recommended season 1 so I wanted to add season 2 to the list. I'm sure a season 2 of Blend S would follow a similar format as New Game!! did, though.