We subscribe to three daily newspapers, one English and two vernaculars: The Japan Times, the Asahi Shimbun and Tokyo Shimbun. JT and TS are delivered to our front door each morning, and like everyone, including non-subscribers, we can access JT's website, with content going back to about 2000, for free. Our Asahi subscription is digital only. Until last July we subscribed to the paper edition. So altogether we spend ¥10,830 a month for news: ¥4,480 for JT, ¥3,800 for Asahi and ¥2,550 for TS (morning edition only; with the evening edition added it would be ¥2,800).
Ideally, we would prefer receiving all our news digitally. Though at the moment physical newspapers are easier to read and browse on a day-to-day basis, they are more difficult to file and reference, especially for work purposes. Most digital newspapers have a function similar to Google Alerts, and with Asahi you can register up to five key words or phrases; every day articles that contain these phrases are compiled separately. We also like Asahi's scrapbook function. You can save articles you want to return to later in a separate folder, and as far as we can tell the number is unlimited. Nihon Keizai Shimbun also has a scrapbook function, but you can only save up to 100 articles.
The search function is less helpful, especially if you're trying to retrieve something from a past issue. Digital subscribers can search up to a year in the past for articles published in the newspaper and up to six months in the past for articles in the digital edition, but from our experience it helps to remember the headline, since using key words and phrases doesn't always work. Also, some features available in print aren't always available in digital form. Once we tried to access an article in the special "Be" section, which deals with financial and consumer issues and is published on Saturdays. When we called the newspaper they told us we couldn't access the section digitally until Sunday, and even then it was only portions.