Custom CSS option and the WordPress child theme, these are the two ways you can choose according to your need. But when it comes to do changes, if you will do any changes to the CSS of the parent theme and go for updatingthen u will lose all your customisation whereas in WordPress child theme all changes will reflect only in the Child theme, so there would not be any mess up with the parent theme while updating.WordPress Multipurpose theme available with WordPress is a great option suits for multiple functionality.
1. Different behaviour during Up gradation:
Up gradation using custom CSS option is really a very big task as it leads to lose all custom styling and changes you have done before. One side you have to lose all custom styling and on the other side you have to update it so fast to avoid the risk of hacking.
On the other hand, in case of WordPress child theme,child theme inherits all the functionality,features and code of the parent theme without doing any changes to the parent theme. Now, users are allowed to change the parent theme without having any risk of losing any data to update the parent theme.
2. Speed of development
In case of custom CSS option all functionality need to be defined, it takes lot of time for development.
On the other hand with WordPress child theme, if you are using good WordPress Parent theme then lots of functionality, features come along with it.So you have no need to code for everything, child will inherit all the functionality, features of the parent theme thus, it will save your time and speed up your development.However, first you have to give time to understand the functionality of the parent theme.
3. Different behaviour in Extendibility
WordPress child theme provides lots of flexibility without having lot of coding to do. You can modify the particular template files and the particular functions without having any changes to other templatefiles.You can add new functionality very easily.
While with CSS option, lots of customisation have to do. It is not so easy to extend.
4. Safe while fallback
With custom CSS option, you have to think about all the possible scenarios and need to code for them. You cannot drop any scenario because changes are too stressful while using CSS option.
While working with child theme, if you forget some scenario then there is always available the functionality of the parent theme as the fallback option. As changes in the child theme will not produce any effect to the parent theme.
5. Need to learn before use
With WordPress child theme, you have to first invest your time to learn about your parent theme. Each parent theme have their own hooks and filters. So before using the parent theme, one has to take knowledge about its functionality, features etc. However, once you get your parent theme functionality, other child themes are easy to build.
Though it is easy to create and use WordPress child theme, you may not always require child theme. This all depends on the number of changes you are planning to do in your templates. If the changes are too minor then certainly you should go for the CSS option, you can create a custom-style .CSS file or can use Custom CSS plugin. If the changes are too extreme then you should go for the child theme. Many themes available at WordPress official website. Pick the one such as WordPress Multipurpose theme which works well with any child template.