In the Modern you will likely end up in a lot of KID and Pirc games, even some Hippo type set ups. Key pawn breaks are c5 for a queen side attack and e5 or f5 for king side attacks. To play the modern you are going to need to know those openings and likely Dragon openings in Sicilian. English you will get Reverse Sicilian, Anglo Dutch, Symetrical games, b5 or d5 played against you. The Botvinnik system gives you options on king side and queen side. But I would not call it slim in theory to have these two as your go too openings. Not that I play them myself. But I do face a lot of Pirc, KID and Hippo type set ups as well as Sicilian Dragon. You are counterpunching against white from a distance. Either they will go to attack the fianchetto, or ignore it completely for control of the centre. The English I do not play yet. But I did look up the theory to play against it. Played Agincourt against it last time and went into a Dutch set up in the past.
English Opening/Modern Defense

I’m curious — does anyone here play the English Opening as White and the Modern Defense as Black?
How well does this combination work in practice?
Would you recommend it?
Im looking for a slim theory opening repertoire and maybe this would be a good fit.
i used to play both.
They aren't particularly similar openings, as the english is relatively safe while the modern often gets very double edged.
Although you don't need much theory in the modern to get by, it is an opening that would require practice to handle effectively.
the english is whatever. You just play moves in that opening.
I’m curious — does anyone here play the English Opening as White and the Modern Defense as Black?
How well does this combination work in practice?
Would you recommend it?
Im looking for a slim theory opening repertoire and maybe this would be a good fit.