Codeigniter is a PHP framework though. Are you asking if PHP is better than PHP?
Having said that: if you use a framework you can be limited by the functionality that framework exposes. Coding a solution yourself does give you complete control but at the tradeoff of simplicity or efficiency (as you don't need to do as much background coding yourself).
Is that what you were asking?
CodeIgniter is an Application Development Framework - a toolkit - for people who build web sites using PHP. Its goal is to enable you to develop projects much faster than you could if you were writing code from scratch, by providing a rich set of libraries for commonly needed tasks. CodeIgniter lets you creatively focus on your project by minimizing the amount of code needed for a given task.
Speed wise, any application written directly in PHP, if written right, is faster than an application written using a framework. If by "stronger" you mean "without bugs", there is a chance that a framework, whatever its name is, could be stronger...
It depends on what you're doing. A framework has the advantage of having 'experts' develop certain modules that you just 'use' - so a lot of the hard graft has been taken out of developing a solution. Unfortunately, most frameworks have a steep learning curve and are sometimes beyond the ability of a beginner - especially those not familiar with OOP and an MVC-type way of working. So, you have the advantage of gaining good security for your level of experience, but you are also at the mercy of 3rd party developers if you don't understand what they've written in their classes.
Codeigniter is one of the more accessible frameworks and it has a loose way of working with MVC - which can be a good or a bad thing.
Now for the not-so-good news - EllisLabs, the creators of CodeIgniter are trying to get shot of it. They haven't released a news item since August 2013, which may be a bit of a worry. There is a thriving community, so patches and fixes may be produced, but major upgrades don't look very likely at this time. I may be wrong, anybody heard differently?