Both are valid sentences, but they have different meanings.
The first sentence means that you are doing something, but it is not an important thing. There is something that is extremely important that you should be doing, instead. We can read it as
(Compared to the thing that we are currently doing), we have things to do that are much more important.
The second sentence means that there are a large number of things that are important. The action you're currently doing may or may not be important, but there are other things that must also be done.
Examples:
(1) I want to go to the movies, but I have much more important things to do, such as my homework.
(2) I've just finished packing my suitcase, but I have many more important things to do before going on holiday; such as tidying up and taking out the bins.
(1) I could stay at this meeting, but I have much more important things to do.
(2) I've been taking a break for a while, but I have many more important things to do.