It's fun to see so many different opinions. Interesting that you mentioned the great library. In my opinion it can often be harmful to build this. If you are going to build a science city it is definitely harmful. With the (not so) great library you will pick up a handful of junker techs early on and it will take extremely long until you discover university and astronomy. After that you will pick up another handful of junkers and maybe two or three techs that you actually need. Now, those junkers are eventually needed later in the game but you can just trade for them with the ai and you will get them for free. In the meantime your research has slowed down thanks to the library.
How useful is Leonardo's? It will turn your warriors and phalanxes into riflemen and your horses to cavalry. You will then save 20-30 shields for each rifleman you want to build and 40 shields for every cavalry. Cavalry is good enough to beat the best defenders out there at the time it's available unless you are attacking a city with walls. Riflemen are not as strong and should, in my opinion, stay at home. So, you can build 10 horsemen and one Leo or 10 cavalry for the same amount of shields. Is an attack force of 10 cavalry enough? No, I'd say you need 20 cavalry and some diplomats to be successful. That's another 400 shields that Leo will save.
OK, what about Michelangelo? To save 400 shields you need 7 cities that require cathedrals. Also, small cities don't need temples. So, maybe if you have 5 bigger cities and 5-10 small size 1-3 cities, then you will save 400 shields with Mike's.
So, if I plan to go to war in the midgame, then I would prefer Leo if my empire is smaller than 10 or so cities, otherwise I would choose Mike.
Let's take another example. You plan to be peaceful and not fight any wars. Then you will need one rifleman for protection in every city and you also want one engineer for each city improving the land. Normally, you aleady have a settler which is about half an engineer. You can then save 20 shields with Leo's upgrade. If you have 2 settlers, then you will save 40 shields. As I said earlier, you will spare 30 shields when your militia is upgraded to rifleman.
OK, that's 50-70 shields for each city. Compare that to 120 shields that a cathedral costs. In the peaceful world Mike is clearly better.
So, my conclusion is that Mike is better in most cases.