The obvious difference is that any book can only teach you techniques for playing the music up to the date when it was written. For example Czerny and Beyer died about 150 years ago, so you won't find anything about 20th/21st century playing techniques, or 20th/21st century popular music.
A good modern book will probably have exercises and pieces from wider range of musical genres. Even for "classical" music, compare Czerny and Beyer with Bartok's "Mikrocosmos" - which isn't "contemporary music" now, but it's very different from anything in Czerny or Beyer.
As well as the musical content, keyboard playing technique has developed a lot since Czerny and Beyer's time. These illustrations from http://imslp.org/wiki/Vorschule_im_Klavierspiel,Op.101(Beyer,_Ferdinand), don't really show "piano technique" at all - that is harpsichord technique. Trying to play modern piano music that way is at best not very effective and will severely limit your progress, and at worst will cause long term strain injuries. (IMHO Hanon's book of exercises should be banned, on health grounds!)