I use and create custom code for e107.
These applications are reasonably secure, remember they are collaborations between a number of developers many of whom will be security conscious. Sure no app may be perfect and if a top hacker decides to target YOUR
website hosting (why would they?) they probably can find a way in. However, most of these things are pretty safe from script kiddies, and probably a damn sight safer than any custom code an amateur like you or I might throw together - surely?! Or if you are a security expert, the code is open source so feel free to review it

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The golden rule is to never trust any user input, some careful use of functions such as preg_replace can help validate any user entry, encode html entities, SQL Server Injection, XSS attacks, etc - we know what to look for! The bonus of using e107 is that it has it's own custom parser which handles these for you, with a wide user base any flaws in the logic are quickly picked up and updates released.
However most of these products are fairly mature now, so real need to worry!
Yes, if you use an out of the box e107 installation you may find your
website hosting lokos a bit like everyone elses. But it is easy to create a custom theme and a unique look for your
website hosting, theming in e107 is very flexible, its not just about changing the colours, its about creating any style you wish. Perhaps this was a problem with old CMS systems but things have evolved a long way I guess. It can be tough to identify the CMS running a well themed
website hosting on looks alone. Creating your own theme takes some time over using an out of the box one, but no harder than designing a
website hosting from scratch!
With custom code (plugins) being created all the time and the abilty to create code of your own at will, you are not limited in any way, however it does provide a load of core features that would be silly to code yourself!
Which one you use is up to you, I trialled a few, e107 stood out to me, but others will certainly disagree. Joomla is getting good press right now (I didnt find it so easy to use). They only take mins to install and setup, so give a few a go.
Cheers, and GL!