You can say both but the nuances are a bit different because of the different meanings. We usually use *like to do something* when we mean that we like the effect of doing it, or we think it is a good idea to do this thing because of its wider effects:

 - I like to have my cavities drilled and filled with amalgam.

This would imply that it's a sensible thing to do. In contrast, we usually use *like doing something* when we find the experience itself pleasurable or enjoyable. Consider this version of the sentence:

 - I like having my cavities drilled and filled with amalgam.

This would tend to imply that you were a bit of a masochist! Nonetheless, most of the time there will be little discernible difference in everyday speech. Both of your comments to each other were very complimentary!