They don't have better detection systems in f2p. Their detection systems are the same in every world. You're just more likely to be banned quickly in f2p because f2p accounts (particularly new accounts) get flagged by the system much faster due to suspicious activity when compared to accounts with membership. However, it still depends on the activity you're botting. A p2p account can still get banned long before a f2p account if it's doing something with a high ban-rate.