Everyone should note that for the most part bottled water is just "tap water" that has been filtered. At $1 plus a bottle (plus the almost always not recycled plastic bottle), why don't people just get a Britta filter for home or office? Filtered tap water is now more expensive than soda!
I'm happy to see you have a slightly better understanding than most of the people I hear complaining about this. I couldn't tell you how many times I've heard that brands like Dasani, Aquafinia, and Smartwater are "just tap water". That's akin to someone saying, "why are you putting gasoline in your car when you can buy a barrel of crude oil for so much less?".
Now that being said, a Brita filter is simply carbon filtration. The brands I mentioned, and many others, are filtered through multistage reverse osmosis units. Typically they start with a 10 micron fiber filter. Then a 5 micron carbon filter, which is probably about what a Britta filter is. The next stage is a 1 micron carbon filter, then through the RO membrane. And usually a final carbon filter. A really effective system with decent source water can get the total dissolved solids (TDS) down to 1 to 10 PPM. The feed water on my system at home is between 400 and 500 ppm, depending on the time of year. Usually the post RO water is in the 5 to 10 ppm range. I run that through a two stage dionization filter that takes it down to a TDS of 0 ppm. I used to keep saltwater invertebrates, so I needed a good filter to mix with salt. Since my tap water was so poor, I started drinking the filtered water and find most water with a TDS above 100 ppm to be pretty nasty tasting. Most of the filtered brands mix in some minerals and usually the TDS is in the 25 ppm range. I'll buy RO filtered water when I'm away from home, but use filtered water for the most part.
I'm not sure what the cost difference is for bottled water, but the fiber and three carbon filters on my system need to be changed every 6 to 12 months and the RO membrane every 4 to 5 years. The filters are $25 for all of them and a the RO membrane is $45. I used to recharge the DI resins, but they're $40 for five lbs. So I don't have to play with muriatic acid and lye any longer. There's also the cost of waste water. In the winter months, when the feed water is cold, the RO membrane rejects about 2 gallons of water for every gallon that passes through. When the feed water is warmer, it will reject more.