Before I reply I have a couple of questions regarding your puppy. First, did the vet do a fecal analysis on your puppy's stool? There are many contributing factors to runny stools, including coccidia, worms, stress, giardia, allergies and more.
If he did a fecal analysis and determined that the food was too rich, it could be the protein content is too high, or he is allergic to an ingredient in the food. Whether or not Natural Balance is better than Wellness- this all pretty much depends on your bully. It took me several food trials to find my personal favorites. (Fromm and AvoDerm) but others here also have much success with Wellness and Natural Balance.
My first question is how fast are you switching foods? For Bullies- especially those with a sensitve stomach, the process must happen very slowly. If you switch too quickly, it will send the digestive system in an uproar and cause gas and stomach pain, diarrhea and bloating.
If you bully has really loose stools right now, I recommend putting him on a bland diet for a couple of days and see if his stool firms up.
Bland diet is white rice, mixed with a bit of boiled hamburger or chicken. You can also top it with a scoop of cottage cheese.
I usually give about 3/4 c of rice and 1/2 c of hamburger myself.
Once I clear out the system, I slowly add dry food back into the diet. Like 1/2 c rice with 1/2 c dog food twice a day for one more day and then the next day back on two feedings of just dog food.
Also be sure you are not adding any unhealthy dog treats into the mix, this will upset the tummy as well. Make sure he is drinking plenty of fresh clean water throughout the day as well.
Hope this helps, and please keep us posted. I am sure you will get much more advice on this. But right now I am the only one online! LOL
Where is everybody??!!