I have a Pur filter on my kitchen tap, and run that into a Britta pitcher, so it's double filtered by two different manufacturer's filters. The water here is very hard. On its own it tastes mildly bad, but not horrible. East-side Madison water was worse. I generally don't detect a bad smell or chlorine in our water, but I did around the last time they reported slightly elevated, but still safe, biological contamination. The double filtration cut through that and left the water tasting nice.
I do think charcoal filtering imparts a pleasant taste to the water. I love the first few pitchers of water right after replacing the filters. That new filter taste does fade after about a week or so, and I replace the filters about every 2 months.