A few years ago I did some research into the whole "New Coke" debacle (as well as having tried the product personally as a young lad, but anecdotes are disallowed here). Obviously it's difficult to effectively describe a flavor, but I can share what consumers and reporters of the day said about it.
At the 1985 press conference announcing the reformulation, Coca-Cola’s CEO Roberto Goizueta famously stumbled trying to characterize the new taste, describing it as "smoother, uh, uh, yet, uh, rounder yet, uh, bolder."
Common adjectives of the day described the taste as "smoother" and "sweeter" compared to the original recipe. Diet Coke was a relatively new product then, having been introduced in July 1982, and many consumers felt that New Coke was essentially Diet Coke with high fructose corn syrup rather than Diet Coke's aspartame sweetener. Some felt it was even sweeter than Diet Coke.
In general, probably the most common sentiment was that it was much sweeter than the original formula, and "more like Pepsi."
New Coke was not actually called "New Coke", it was just "Coke", with a label reading "new" on the can. When Coca-Cola Classic was introduced after a mere 79 days, new Coke was renamed "Coke II".