Yours is a huge question that would require a book to answer. The title of that book is Yeast, written by Jamil Zainasheff and Chris White. White is the founder of White Labs, so the book is expectedly biased towards liquid yeast. This bias aside, it's the best volume available for learning how yeast works and how to work with it. Highly recommended.
But I'll offer my own limited, anecdotal answer. I've brewed with both White Lab's WLP001, Wyeast 1056 and Fermentis Safale US-05, which are all the same strain. And I've brewed the same recipe pale ale using each. I've noticed no difference in flavor between the two former, liquid yeasts, both of which were made into 1500ml starters before pitching into 5 gal batches. But I brew with US-05 considerably more often because it's more readily available where I live. I've found that there is a slight difference in the flavor profile using this dry yeast; it has very slightly less depth of character. That said, it's flavor profile works well for the beers I'm fermenting with it.
My personal belief is that the packaging of the yeast (liquid or dry) isn't as important a factor as how it's handled before and after pitching. For liquid yeast, a properly sized starter is supremely important (make sure your starter wort is ~1.043, has a yeast nutrient added, and is provided lots of oxygen). For dry yeast, rehydrate it prior to pitching, paying close attention to prescribed temp ranges. (I once pitched a packet of dry yeast straight onto wort. That ferment was less than stellar and the resultant beer was less than it had been using rehydrated yeast.) And of course how it's handled after pitching is the most important factor in making beer: Temp control. Temp control. Temp control!
