Answer: Both, or either. Whichever suits you the best at any given time.
Moodle is best if you have a large number of resources that you want to present in an organised way. Particularly if you have students working towards an external, you can present lots of rich resources whilst teaching the module, and then they will still be there when students are revising at year end. Seems to work particularly well in the sciences. Also great for resource re-use. Set up your topics one year, and then you have a great base for subsequent years - just hide topics and resources as you need (by clicking the little eye).
Google Classroom is best for creating collaborative tasks, for giving students templates to work in, for having a quick view of what students are currently working on and generally for all quick-n-dirty daily interactions with your class.
So basically, Classroom is more interactive and Moodle is more organised. I use both, as sometimes I need organised resources, and sometimes I need to be working closely with students on the work they are doing.
There's no hard rule - Classroom can organise your resources by topic and Moodle can provide interaction. Many teachers largely stick with one or the other. But you will probably have an easier life if you use each tool for what it is best at!
One final point though - we have a requirement that for all senior courses, the assessment schedule and weekly planner are available on the subject Moodle page. Being consistent about this is important as it helps our students be organised in setting goals and preparing for assessments.