A warble is created by "inharmonicity" in the first several overtones. That means they are
out of tune with one another and the stronger harmonics have a tug-o-war over which one controls the "regime of oscillation" which simply means the sound that you hear which is a combination of the fundamental and it's harmonics. The
warble is the sound created when the control goes back and forth between two harmonics that are out of tune with one another.
This raises the question of what causes the "inharmonicity" of the overtones in the first place. I know that one of the causes is the mismatch between the "effective volume" inside the mouthpiece and the volume of the imaginary "missing cone" that would exist of the taper of the neck (crook) were extended till it made a point.
Here is what I would suggest. Take a piece of duct tape and cover the portion of each mouthpiece where the reed sits. Fill the mouthpieces with water to the top of their shanks and then pour it out into a graduated cylinder. Record the interior "physical volume" in milliliters (ml) which is the same as cubic centimeters (cc) and compare the "physical volumes" of the two mouthpieces.
If you want a very exact comparison measure how far each mouthpiece goes onto the cork in mm to play in tune. Then measure the interior diameter of each mouthpiece's shank also in mm. Use the formula pi r squared x height to determine the mouthpiece volume displaced by the neck---where the "height" is the distance the mouthpiece goes on to the neck. Then subtract this amount from the measured volume of the total mouthpiece.
My hunch is that the Bari Esprit 2 mouthpiece's volume is the larger of the two. If my hunch is correct, push that mouthpiece onto the cork until the warble goes away. If the Bari Esprit 2 mouthpiece's volume is the smaller of the two, pull the mouthpiece out until the warble goes away.
Here are some sound clips of a warble I recorded at regular speed and slowed down. The warble was produced using a tenor sax mouthpiece on a C-melody.
Warble Regular Speed
Warble Slow