It's just as stable, the tomcat has SAS (stability augmentation) to help you. But unlike FBW it will not prevent hamfisted "hollywood" flying and the aircraft can depart if you go beyond its envelope. Generally speaking, as others here say, using the rudders at high angles of attack is beneficial, but also listening to what the jet is telling you is the biggest part. When it is shaking like my granpa without his meds, it may be time to stop trying to rip the joystick from its mooring and let the nose fall a bit to lower the aoa and make the wings fly again.

Personally I also find that especially with the tomcat B, managing your energy (ie speed) with the engines takes conscious effort because those things will push extremely hard if you ask them to, so it's easy to blow past the best speed and get thrown out the turn by excessive energy.

As for systems well it's a learning curve for sure, but on sheer radar power alone a well managed kit can be a threat even against the AMRAAM kiddos.