ICU care plan

What do you mean by "which diagnosis is better"? Impaired Gas Exchange takes priority over Ineffective Breathing Pattern because Impaired Gas Exchange is dealing with the chemistry and what is happening in the alveoli (cells) of the lungs while the Ineffective Breathing Pattern deals with the physical mechanics of breathing. If you are asking which diagnosis should you use, that depends on what your supporting evidence is, none of which you included. All diagnostic choices should be based upon the evidence that you have to support them. The evidence supporting the existence of each of these nursing problems (diagnoses) is different.

There is a nursing diagnosis called Dysfunctional Ventilatory Weaning Response. Why don't you use that diagnosis, assuming your patient has the evidence of that problem?