What should I look at before I change tarrifs

Petite

I just need some advice please before I try to change a tarrif over online.
recently speaking to my supplier I was advised to change tarrifs as the tarrif I am currently on the prices have gone up and there is now a new online tarrif I can try. (incidently I am confused why they do this put the price up and then introduce a new cheaper tarrif, it's very confusing)

I'm on click energy 5 for Gas and electric and the advisor checked the prices against Web saver online 2 and found that although my current gas price was cheaper I would save money by changing my electric.

I didn't know I could have different utilities on different tarrifs but she assured me it was okay. And I could make the change myself online by logging into my account.

Anyway I just want to know what I should be checking before I do this.
Any help or advice muchly appreciated.