Which test would be more reliable in detecting gallbladder problems abdominal ct scan or ultrasound? which can detect more conditions?

Both are good: This is an age old question. They are both good to look at gallbladder. Advantage of Ultrasound is faster and convenient. CT gives more information about pancreas and other structures in abdomen which are NOT visualized by US due to gas in the gut. I would say if you are ONLY looking at biliary tract and gallbladder start with US otherwise get CT.