Your partner will already have opinions about what is worth seeing and what isn't. And these ideas may or may not be in sync with what you want to see. Traveling on two completely different budgets will surely cause problems while away as one person is required to spend less than the other. Are you traveling for different reasons. Because you are together all day, every day, traveling can break even the best of friendships.
Small habits seem to become larger.
Decision making and agreeing on daily plans becomes more and more difficult. But dealing with such problems is not entirely impossible. You can make the itinerary for one day and then your partner can plan the next day. This strategy removes any blame for a seemingly poor decision. Make equal contributions before-hand and then use a credit card to access the money.