Should I go for a better paying job or stick with one with strong company branding?

I would suggest you stick with it for now. Because you managed to get this job with your Music diploma, which is considered not relevant to your current job. This job will give u experience in admin which you can use for your next jump unless you intend to find a job following your area of study.

Stay a few years and see if you can jump elsewhere. Of course, if you decide that higher pay is more important now, then you can try going elsewhere but take note if you are looking for job that is not your area of study, it will be harder to find.

Big 4 Firm pays well for accountants and auditors, doesn't mean they pay admin and other job positions better. (But I do hear that the bonus based on number of months are quite generous to the non-core positions too)

If it's your first job, don't worry about the pay... or the brand of the company.

Focus on what you can learn in the skills at that company.

Focus on the long term, the money is very insignificant compared to the potential you can get in a lifetime from skills you acquire early.

Think Long Term.