Controlar 4 Servos con dos Joystics

No estoy de acuerdo, eso tiene que funcionar. Si no lo hace es porque tienes algo mal conectado.

Acá junté todas las sugerencias

#include <Servo.h>

Servo ServoHorz0;      // Create a servo object for the pan (horizontal) servo
Servo ServoVert0;      // Create a servo object for the tilt (vertical) servo
Servo ServoHorz1;     // Create a servo object for the pan (horizontal) servo
Servo ServoVert1;     // Create a servo object for the tilt (vertical) servo

const byte s0horPin    = 8;
const byte s0vertPin   = 9;
const byte s1horPin    = 10;
const byte s1vertPin   = 11;

const byte horzPin     = A2;   // Analog input for the joystick horizontal axis
const byte vertPin     = A3;   // Analog input for the joystick vertical axis
const byte horz1Pin    = A0;   // Analog input for the joystick horizontal axis
const byte vert1Pin    = A1;   // Analog input for the joystick vertical axis

unsigned int horz0Val;          // Value read from the horizontal axis
unsigned int vert0Val;          // Value read from the vertical axis
unsigned int horz1Val;         // Value read from the horizontal axis
unsigned int vert1Val;         // Value read from the vertical axis

/* Setup */
void setup() {
  ServoHorz0.attach(s0horPin);  // Use pin 9 PWM output for horizontal servo
  ServoVert0.attach(s0vertPin); // Use pin 10 PWM output for vertical servoç
  ServoHorz1.attach(s1horPin);  // Use pin 9 PWM output for horizontal servo
  ServoVert1.attach(s1vertPin); // Use pin 10 PWM output for vertical servo
}

void loop() {
  horz0Val = analogRead(horzPin);           // Read joystick horizontal position
  horz0Val = map(horz0Val, 0, 1023, 0, 179);// Scale reading to suit servo
  ServoHorz0.write(s0horPin);               // Move servo to required position
  delay(15);                                // Give the servos time to settle
  
  vert0Val = analogRead(vertPin);           // Read joystick vertical position
  vert0Val = map(vert0Val, 0, 1023, 0, 179);// Scale reading to suit servo
  ServoVert0.write(s0vertPin);              // Move servo to required position
  delay(15);                                // Give the servos time to settle
  
  horz1Val = analogRead(horzPin);           // Read joystick horizontal position
  horz1Val = map(horz1Val, 0, 1023, 0, 179);// Scale reading to suit servo
  ServoHorz1.write(s1horPin);               // Move servo to required position
  delay(15);                                // Give the servos time to settle
  
  vert1Val = analogRead(vertPin);           // Read joystick vertical position
  vert1Val = map(vert1Val, 0, 1023, 0, 179);// Scale reading to suit servo
  ServoVert1.write(s1vertPin);              // Move servo to required position
  delay(15);                                // Give the servos time to settle
}

Tenías varios errores.