I use both. My logs are primarily paper, but I don't carry my paper logbook on the road (where I'm usually found). I do carry my computer. I use logbook pro to record flights on a day to day basis, as well as filling out paysheets, perdiem requests, etc...all of which document where I went and what I did on a given day.
When I do get home, I transfer everything to my paper logbook.
My logs are far from just legal documents. They are journals that record what I've done with most of my teenage and adult life. They contain pictures, photographs of some airplanes, some places. Every medical certificate I've received is glued in the back of each log. Each of my government authorization cards is there. Momentos are there. Business cards are there, from various places I've flown and worked.
Logbook entries are detailed. There's little to remember about a flight that went from A to B, but it's the details that give life to each moment aloft. Perhaps a gusty landing, perhaps an equipment failure, perhaps a unique sunrise. When doing ag work, I include the winds (drift issues and claims); these have come in handy later when someone tried to claim adjacent crop damage from drifting chemical. I include notes about instruction given in detail; this has saved me from legal and FAA action by including particulars which exonerated me during an investigation.
Electronic logbooks are impersonal, business-like. One can jot down the same words, but one can never have the same flavor. Electronic logbooks are imaginary bits and bytes that can vanish in the presence of a magnet. Paper logbooks age and drift in character and save for fire or flood, are treasured records of one's life that with luck and some care will last long beyond one's own sorry career.
Having spent years of my life in flight, what have I to show for it, but my logs? I traded my life, quite literally, for those experiences, and the log is the record. The paper log is the scrapbook, the memory, and the accounting of my time, whereas the electronic one is simply an expedient ledger that shows currency and qualification.
As far as filling out an application, I do it from the paper logs. I haven't managed to transfer all my paper logs to computer. I'm sure if that eventually happens, then the flexibility might make classification of flight time easier...but it's not that difficult now. How you log your time, and the categories you create in the blank columns of your log can make the task of breaking down your time on-demand, much easier. So far, it's not a problem. More to the point, one needn't break one's time down to the last decimal point when filling out an application: one can come close with a guestimate, then turn logs over to the interviewer and let them see for themselves. The employer makes a cursory review for reasonableness, and moves on.
So far as the log itself in an interview, I've had plenty of potential employers take an interest in the photographs, some of unique aircraft, that make for both an ice breaker and a conversation across an interview table that wouldn't take place without the book. The electronic logs are handy, but the paper log is the one real record I have, and one of my most valuable assets.