I have only been making cheese for about a year now, but I have made a lot of cheese and have had the opportunity to work with a lot of raw milk. The cow is now dry and probably will not calve until September, so it is probably 7-8 months before I have that regular supply again. I have also made a lot of cheese from store bought (mostly Costco) milk. I have probably done about a 50/50 split of Raw/HP. My observations are:
1. Raw milk is much easier to work with. Given like conditions, the curd set is much better than using HP milk with CaCl.
2. There is a definite difference in flavor and complexity of the mold ripened cheeses, and to a lesser degree, mozzarella.
3. I was surprised that my Stilton #2, made with Costco milk, tasted just as good as my other Stiltons so far, all others made with raw milk
4. The few hard cheeses I have made with both so far , mostly manchegos, I cannot detect a significant difference in flavor or texture. The same can be said for feta.
It is my opinion that for the cheeses that are aged there will be less difference, as much of the flavor and complexity of the cheese is the result of the slow breakdown of fats and proteins, while in cheeses that are eaten younger there is more impact from the character of and indigenous micro flora in the raw milk.
Do I think one can make great hard cheese with store bought HP milk? Absolutely. The vast majority of cheeses in the world are made with pasteurized milk, and it is pasteurization that upsets the calcium balance and makes the milk more difficult to work with.
Getting back to the initial post, if you were over renneting your cheese, particularly if you were using vegetable or microbial rennet, it can account for a bitter taste. I was told by a master cheesemaker that you should only use animal rennet for cheeses that will be aged for more than 6 months. The other rennets contain compounds that add bitter flavors to cheese as they break down over time. I suspect your success with the raw milk is due to a combination of your more conservative use of rennet and the fact that raw milk is easier to work with and more forgiving of technique than HP milk.