I've played essentially every Mario Golf and Everybody's Golf game so I feel like I can field this one.
This game is extremely similar to Mario Golf. If you like Mario Golf for reasons other than the Mario IP itself you will love Everybody's Golf. The controls are essentially the same (except that the method of putting spin on the ball is slightly different between them - in Mario Golf you change the button you press to end your swing, in EG you hold a direction on the d-pad) and the things you need to pay attention to before the shot - distance loss in the rough; uphill / downhill lie; wind speed and direction; fliers etc - are all roughly equivalent between them.
The most major difference is in the course design - Mario Golf tends towards more simple holes tricked out with Mario-centric features, traps and obstacles. Everybody's Golf, despite the anime look, tends towards more intricate, realistic hole designs, though ones that become more difficult than what you'd see in real life by the time you reach the last course. I find the course design in Everybody's Golf massively superior, to be honest, and it's why I prefer this series.
Neither game has an extensive single player mode - you just enter tournaments to level up and unlock new courses. Which is enough for a golf game - you're really playing to beat your own scores or playing other people online, after all.
Everybody's Golf has a lot more levelling systems - in the past you levelled up a character to unlock more power shots and 'super spin' abilities which activate if you hit the pin. In this one, you create your own character and then level up each club in the bag as you hit good shots with it. I don't particularly like it as you need to grind to get a good set of clubs and start hitting good scores, but for those who like a sense of progression that'll really keep you satisfied.
That's about it, they're really, really similar. Couldn't recommend EG games enough to a Mario Golf fan.