CodeIgniter has been the most preferred and still is currently the most preferred PHP framework for building simple websites rapidly. Reason been, CodeIgniter is relatively easy to use and understand. It has what I will term by far the best documentation for any PHP framework. Plus it also has a very large community base meaning you can be guaranteed that it is stable and been tested by many users.
Any issue you might encounter has probably already been solved by someone. CodeIgniter looks so simple that you do not even really need to know much about PHP in other to understand how to use it. Code igniter also requires almost no configuration to get started with using unlike other PHP frameworks. Over the past few months, there has been a lot of debate about CodeIgniter been dead. Different developers gave different reasons for this. Code igniter I would say should be used if you intend to support only php5.2. CodeIgniter is said does not support php5.3.
On most occasions CodeIgniter has to get external libraries to perform certain operations e.g. templates, authorization library. Libraries are loaded as singletons and use magic.
CodeIgniter does not support things like ORM, ODBC driver, class auto loading just to name a few.
In terms of code modularity, CodeIgniter is considered to be one of the worst performer. Code modularity can be described as you not having the capacity to allow a framework import other package into your application or not supporting the HMVC pattern. Some people however say these are not points to judge a framework on. Due to the lack of modular design patterns, CodeIgniter has to rely on third party developer libraries.
Laravel is a new PHP framework which currently making a lot of waves. It is designed by a guy called Taylor Otwell. The Laravel community is still small, but it is growing very fast. It supports PHP 5.3 meaning all the new goodies in PHP 5.3 can be used in it. It is more object oriented compared to CodeIgniter. So your not an object oriented developer, you might want to familiarise yourself with OOP. Some of the advantages of Laravel is the powerful ORM which is built into Laravel unlike CodeIgniter where you have to use third party Spark, etc. Laravel also has a built in authentication, to achieve authentication in CodeIgniter, you have to use spark.
Laravel is still young, but seem to be maturing very quickly. It can be seen as either a good thing or bad. Some people prefer a rapid development approach, while some prefer a slow stable approach.
Many developers do not like Laravel, because it changes quickly. At the moment it is already on version 4 which is a very big release compared to version 3. There is the fear of compatibility issues due to the very fast development period so they are waiting until they reach a point of stability. One other major thing to know about Laravel is that Taylor is the major develop. So what happens if one day he gets bored of it?