Buying both is good as the gaiwan gives an honest taste of all teas and good for trying out a new tea. The yixing clay teapot improves the taste of the tea through it filtering and breathing functions. But make sure you buy the right size teapot the type of tea you make and for the amount of people you make tea for. If you drink different kinds of teas (i.e. green, black, pu-erh), then it would be best to buy 2 or 3 different teapots, as each tea has its own unique flavour and the teapots for making each tea is of different density.
I would vote for both too, different situations may make one better while another situation makes the one that was less good last time better next time.
But if you only can afford one (now) I would go with gaiwan becouse it fit more situations atleast quite good.
That depends on what tea you prefer too. If its white, green and yeallow teas or even scented teas then go with the gaiwan. If it's oolongs and pu-erh a yixing teapot is the best. I don't drink much black tea but I guess it's 50/50 between them