I would say that estimate for disposables is possibly high, depending on whether you buy in bulk. Buying from Costco runs about $500/year for our 1-year old, so the total cost will probably be between $1500 and $2000.
Cloth diapers are definitely cheaper if you own a clothes washer (or are willing to wash in bath tub or something) and either a dryer or have enough diapers (or dry enough climate) to line dry as quickly as needed.
If you have coin-op laundry and live in a humid climate, the numbers start tilting. For us, running a wash cycle costs $1, and dryer is 25-75 cents depending on load size. The costs are relatively low for coin-op because it's in a condo - I've seen coin-ops as high as $2.50 for a wash cycle and $2 to dry. With 10 cloth diapers we would need to do a load of laundry (and use the dryer) at least 2 of every 3 days (compared to 2 loads once a week that we normally do). With 15-20 we could line dry some or wash less often. With our laundry costs, cloth diapers would still come out ahead, but not by very much (not enough for my wife to consider it worth it, since she does the majority of the diapering and laundry). If we had to use a laundromat, the even higher costs would put disposables ahead financially, as well as being enormously inconvenient.
We're planning to rent a house before our 2nd child is born later this year, with washer/dryer hookups, so we'll reconsider cloth diapers.