My personal opinion: If you have say 100 instances of the same application that could be a nightmare to maintain (bug fixes, upgrades...). You would be better of having one app (and one database) but you have to be careful to make each user's data and login secure. So particularly the database part and access to it has to be thought out well.
broj1
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Hard to say. If you have one app and one database you have only one database connection but I am not sure whether this is better or worse. As far as scripts go I guess with caching you'd be better of with one app than with many apps but I have a feeling that the difference would be very small. Please note I am only guessing since I have'n got the experience to compare. I hope some other folks with more mileage will contribute to this topic.
broj1
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Depends on what you're using. Are you using java or PHP or something else?
Everybody with their own downloaded client would be the fastest (probably), but you're talking JAVA or something else that allows client-server communication. If you want to use PHP client-ways, I think you need to use PHP-GTK - which I find extremely unwieldy and poorly documented. In addition, as broj1 states, updates and upgrades can be problematic. However, there are certain sites that guide you through app building with Android/java and iPad/objective C. The problem of course is that you have to develop the app in a number of languages for decent coverage.
If you have cloud hosting, I imagine that your bandwidth / concurrent users is not going to be a problem? Many factors affect speed of an online app/site and you seem to be expecting heavy traffic, so ensure that your code is lean and doesn't make needless calls to DBs, files (e.g. js/css) and that your images are as optimized as possible. The traditional web-based site has many advantages, including a single update/upgrade location and you only need to write in your preferred languages - although a responsive layout is almost essential these days for tablets and mobiles. There are many bootstraps that can do this for you.
Whichever way you go, again as broj1 states, security will be paramount. This are just a few thoughts, and I am in no way an authority on the subject. Caveat!
diafol
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