Older post but some comments

Gimbal unit is expensive and heavy especially where the pressure thrust is high either due to pressure or size or both. Universal is relatively cheap compared to gimbal units. Double gimbal requires more space.

Both types, e.g. universal having 2 bellows elements and double gimbal can have lateral movement in all directions. External axial movement is zero excluding the rod expansion if the rods go over both bellows elements. If there are two sets of rods the center pipe expansion has to be considered in a same way as for the double gimbal.

There is a difference in rotation. If the universal has 3 or more rods all rotation is prevented. If universal has 2 rods then the ends can rotate around one axis. Take 2 sticks in vertical and try to balance a plate on top of them. Take 3 sticks and try again. Expansion joint works the same.

Gimbal unit can rotate in all directions, e.g. one stick supporting the plate.

CAESAR II modelling for the universal has to be correct. Do not use simple modelling for 2 rod case. If you do the result is wrong. You do need to use comprehensive modelling so that the ends are free to rotate around one axis.

When you use 2 rods you have to make sure that the rod orientation is given on the drawing. I had a case where original rod orientation on turbine connection was vertical. Changing it to horizontal and doing the right modelling nozzle loads dropped substantially.