Whilst many purists would immediately slap the iPhone out of my hand, thrust a pen and paper into my fists and insist I 'do it properly', I feel there is a lot to be said for the convenience of applications such as Battlescribe, Army Builder and their ilk; they solve all the complicated mathematics for you, have a repository of all the units available (and frequently most of their special rules and profiles too) and therefore save the user a great deal of time that would otherwise be spent flicking through pages and pages of army books or codices, and time spent working out and checking calculations.
In addition, the app saves the data on your phone - you no longer need to lug a large notebook with you when you go gaming, saving carry space for the many rulebooks, army books, codices, dice, tape measures, Cheetos and Doritos gamers invariably bring to the table.
This also makes lists much easier to share with friends and groups; instead of having to meticulously type out your lists, you can hit a single button and paste the whole thing into a Facebook comment for all your friends to enjoy (or foam at the mouth over once they see you've managed to sneak three D-Weapons into your 40k tournament list).
Apps are becoming an increasingly popular method with which to create lists these days, as even desktop PC versions become more and more prevalent.
This therefore begs the question; why (apart from obvious circumstances such as not possessing an iPhone or similar) would players prefer pen and paper over an app, when apps are apparently so much more convenient?
Personal touch & history
Writing an army list is a huge thing to most players, whether they're a full-on historical re-enactor painstakingly recreating Caesar's legions at the siege of Alesia or a diehard tournament nutcase who's busy pouring over his latest tear-inducing creation.
Regardless of your playstyle or motivation, the creation of the army list itself is the first step to creating the army as a whole; with creativity being such a major part of the wargaming hobby, it seems only fitting that even parts which don't involve direct contact with model soldiers be as diverse and subject to the whims of mad gamers as model construction should be.
Creating army lists on paper has been a traditional staple of the hobby for decades, dating back to wargaming's roots as a spinoff of pen and paper RPG games like Dungeons and Dragons. Indeed, go back thirty years or so and a wargaming table would have looked surprisingly similar to the D&D table next door; albeit with more figures and slightly less players per game.
Paper and bookkeeping are a hereditary part of wargaming culture, and with a move towards larger condensed rulebooks containing all the necessary charts and tables, plus the advent of apps, they are sadly dying out.
Even in the tabletop RPG scene, more and more players are turning to editable PDF versions of character sheets and the advent of online RPG services (such as Roll20 - a very useful website for playing pen and paper RPGs online), which sees a greater shift towards electronic-only games (a concept that, rather hubristically, flips a finger to the whole concept of a 'pen and paper RPG').
Having said this, I myself don't feel much nostalgia for the old handwritten army list. Whilst an RPG character sheet is predominantly physical descriptions, gear, mannerisms and quirks, a tabletop wargaming army roster is almost exclusively a maths exercise.
I unashamedly use army creation apps with no qualms myself; whilst creating an army is fun, putting the list to paper and calculating the mathematics was always an immense chore. I find the interface of my personal favourite app (Battlescribe) friendly, convenient and immersive; as such, I actually find creating a list using the app far more engaging than when I use paper.
For the record - I personally always use physical paper when playing an RPG; I hugely dislike using electronic copies, though this is mostly due to the nature of character sheets, as they frequently need to be edited and updated on the fly and bringing a whole laptop to alter a PDF is vastly less convenient than simply scribbling away with a pencil.
To sum up this point; I believe it comes down to personal preference.
Whilst it is a true and sad fact that an element of gaming is slowly dying a death, I believe it is simply being fazed out for something more convenient.
I would never belittle the nostalgia crowd for sticking determinantly to the pen and paper method of creating a list, however, as I strongly believe players should be free to use whichever method best suits themselves.
This does however segue neatly into my second point;
Convenience and reliability
As already discussed, there are certain elements of convenience one cannot disagree with in favour of the app; quick and easy access to rosters with no page turning, self-calculating mathematics etc.
However for every point we award the app we must award at least as many to the humble pen and paper.
The first and most obvious point; paper doesn't run out of battery - this stalwart argument of book-lovers everywhere, touted during disagreements with Kindle owners is certainly just as valid here. Phones and tablets run out of battery; paper does not.
Whilst one could counter-argue that most apps allow the user to print directly from the page, this partly defeats the point of the app and its ability to be taken anywhere at any time.
It is a true fact that many tournaments enforce a rules clause whereby users of electronic army lists may be disqualified if their device loses power and shuts down during gameplay. In addition, many more require a physical copy of a list regardless of the medium you use during the game.
One must also consider that in larger games, you might not have the entire list memorised:
"Did I equip both squads with anti-tank grenades or just one?"
"Did I buy upgrade X for vehicle Y?"
With a dead phone and no hard copy of a list, you could end up cheating yourself or the opponent out of an advantageous situation.
Examining these points leads one to realise that apps are perhaps suitable for friendly play only, where your opponent is already familiar with the list you use and no harm is done if the device runs out of juice halfway through play - where an extra 'forgotten' upgrade here or there makes little difference.
The other factor that must be considered is the reliability of the source; whilst it is convenient to have your iPhone calculate the mathematics for you, figuring it out for yourself gives you a much better grasp of where your points are being spent. In addition, there are frequently errors in the rosters featured on apps; whilst they are being constantly updated, this can lead to (completely unaware) players over or under spending when purchasing units or upgrades. If you copy the points costs directly from the codex or army book onto paper, you can be sure the figures you are using are correct.
Apps also sometimes allow illegal combinations of units or upgrades, perhaps allowing you to take multiples of something that are single purchase only. Alternatively, they may lock out options that are intended to be taken multiple times after a single purchase.
Conclusion; whilst the app provides the convenience and ease of self-calculating maths, only the codex or army book can be trusted implicitly to provide the correct values and ratios for points and upgrades. In addition, the app's ability to share lists on social media is irrelevant whilst playing in a tournament setting, where paper copies of lists are required at all times in the interests of balance and fairness.
To sum up
To reiterate a point I made earlier in the post, I believe this all comes down to player choice.
I myself love using the army creation apps for convenience, particularly whilst away from a desk - building lists while waiting for a train or trying to kill some time between sets at the gym is a wonderful procrastination tool.
Others (particularly more veteran players) would prefer the pen and paper method, citing the reliability of physical copies and the joy of creating army lists by hand, as well as the accuracy of copying directly from the book.
On balance, I feel players should try both methods. Give the apps a go if you can; they're worth a try at the very least and certainly something I feel improves my gameplay experience.
However as a final thought, I would always advocate new players begin their wargaming career writing their lists out by hand. Get a feel for how army list creation works and understand the process so you fully comprehend what it is the application is doing whilst you use it. Also, if we want to preserve the tradition of pen and paper lists, a good start would be to encourage their use amongst new players before introducing them to the wonders of the App Store or Google Play...