Yes........No......and Yes!!!!!
Yes they hold much of the same information....... The Dope card is quick reference fast, simple, easy. The Range Log should be your detailed information gathered during practice, you use it to make the Dope Card for when you need it fast.
No they do not serve the same purpose........ see above!
And Yes you need hard copies of everything....... Yes, electronics fail, batteries fail, and sometimes you just don't have the time. Now that being said only you know what kind of shooting you do. If your only shooting for you off a bench at your range when you want to, then no you don't need a dope card per say. The electronic will do all you need, I would still have the Range log to record hits, misses, and info for the solvers, you'll need it someday trust me. If your a hunter then the Dope card is a must. When dinner presents itself at 254 yards broadside and gives you the wink you don't want to have to fuss with your kestrel or dig out your phone!!!!!