Nearly as old is quite a fuzzy statement. The reality is that Tokyo only had a single line (Ginza) until the mid sixties and started operating in the end 1920s, period during which NYC subway grew several lines. Additionally, the first subway line in NYC still in operation today is the BMT Jamaica Line, with first trains running in 1885.

So actually, NYC rail is much older than Tokyo's. Could it be cleaner? definitely.