A few major differences:
1) The quality of the tea in filter bags tend to be among the lowest. For Western black teas, under the Crush-Tear-Curl grading, filter bags usually contain the lowest or second lowest grade, i.e., tea dust and fannings. Nowadays, some merchants have decided to offer premium filter bag teas with higher grades of leaf, although in general these are still not as good as loose leaf tea. (Note: loose leaf tea has a huge variety of grading as well but I will not cover that in this question. Beware of merchants who claim that all loose leaf teas are 'whole leaf'.)
2) One effect of this quality difference is that tea from loose leaves tastes generally better than tea from filter bags. First, because the fuller leaves allow for a more complex and interesting flavour, and second because the intensity of flavour reached is higher, without introducing as much astringency into the tea liquor. Another related effect is that since filter bags contain smaller pieces of leaf, they yield their flavour more quickly and require less steeping time (longer steep times will result in astringency and bitterness). All these tend to result in a significantly higher price for loose leaf tea compared to bagged tea (although some of the markup is also due to other unrelated factors like branding and snobbishness, particularly for posh retail brands which are often not the best places to go to for loose leaf teas!).
There's been a recent fad of using loose leave teas in fancy filter bags (pyramidal mostly) which is said to be a way of combining the good taste of loose leaf and the convenience of filter bags (the fancy bags are said to allow loose leaves to expand much better than traditional filter bags). Naturally this cannot be 'better' for flavour than just allowing loose leaves to brew in a pot, but it is an option these days, hence 'bridging' the difference between filter bag tea and loose leaf tea.
Lastly, try the two yourself and see! Nothing beats firsthand experience for gaining understanding.