You can watch this one without having to watch the first (however I did and liked the first as well)

I'm quite fond of the Medici's history and I appreciated these two italian series for what they are: a fictional product inspired by historical characters that celebrates them, but doesn't have the goal to be a documentary. It's a homage without the presumption of being the one and only truth. If you want to know more about the real people, read history books (tho, sometimes even historians have more fiction in their books than actual facts, but this is another issue..). I think this series has nothing to envy from other historical tv shows: the cast is great, music and cinematography excellent. In terms of flaws, it does have many of course. Characters arcs are a bit doomed by the fact you have relatively few episodes to develop them. Also, I think that while I appreciate the cast includes talented italian-born actors too - since it's about italian's culture, history and people - I noticed a pattern in that the italian actors are only cast for secondary roles.

As for the differences with the 'real story', you have many because the writers have to still create their own fictional world around these characters otherwise it would be boring and predictable. I, however, find the differences are, for the most part, functional to the narrative and this version of the characters thus the writers' vision. In general, I think it is easier to notice the differences in known real life events that may get changed (there are many. And let me say that Lorenzo is a bit too much a saint here..), than the personal life of Lorenzo and the other characters because those are aspects that, we like it or not, we don't really know so much about and what we know is, for the most part, only speculations from historians that don't always base them on concrete evidence. For example, some may complain that this series romanticizes the relationship between Lorenzo and his wife Clarice, but is that aspect really the most unbelievable thing? The two had 10 kids together and in a time where men having lovers and illegitimate kids was considered almost the norm in society, Lorenzo had none. His father and grandfather did, Lorenzo didn't. The only lover we kind of know he had is Bartolomea Nasi, whom he had relations only years after his wife's death anyway. We know from the correspondence between him and his wife, as well as accounts of friends, that Lorenzo had a great affection and respect for his wife (as well as his kids and the rest of his family). If we know that she was a sweet woman and important to him, it's because of his own written words (most touching is the letter he wrote after her death where he expressed authentic grief and sorrow over the loss). He may have not written poetry for her (which isn't surprising because "amor cortese" poetry traditionally excludes marriage for specific reasons you may not understand nowadays but made perfect sense at the time ), but some of their correspondence is, perhaps, more authentic in its lack of fanciness and as an expression of affection than most of his poetry for other women is. It may have been an arranged marriage, like most where at the time, but it doesn't mean it was a loveless one on the long run so I don't find their relationship in the series is the most far fetched thing (even the first time he saw her is, I think, a little nod to a letter written by Lorenzo's mother where, upon meeting the girl for the first time as a possible bride for her son, she said he had seen the girl himself and it seems she had made an impression on him). The series ending credits include some historians whom the writers consulted, I guess those are among the ones who, using sources, simply have a different interpretation of their relationship, along other personal aspects, than how previous narrative products about Lorenzo had romanticized and 'invented' his private life before. In short, you can't criticize the writers just because their story may not align with romanticized stuff made by others.

After all, even other aspects are romanticized in the series as much if not more than the relationship between husband and wife. Like I mentioned before, Lorenzo is far more a 'good boy' here than he was in real life. His 'lover' Lucrezia Donati is portrayed as being his mistress here but in real life, she never was his lover, as his love for her was only platonic, and he even was the one who helped her father find a husband for her in the businessman Ardinghelli. Yes, he wrote poetry for her and it is important and makes it reasonable to believe that she probably was his first love, but people should take it in context and not make the huge mistake of wanting to project a modern ideal of romantic love on their relationship. His poetry for her followed a long established tradition by Petrarca that celebrated platonic love and she was, in many ways, one of the popular girls of his time that he choose for the purposes of amor cortese, as it was the trend for all the guys in his circle to have one. Real life, however, is another thing and aside from Age of Innocence speculations, there is no proof there was any relationship between them before and after he married miss Orsini. In fact, if you are looking for realism, perhaps it would be more fitting to represent them like they represent the connection between Botticelli and his muse Simonetta. Speaking about Simonetta, we know that her relationship with Giuliano is romanticized too because in reality, it's likely that the woman he actually was in love with, and whom he had an intimate relationship with during the historical time developed in the series, was in fact another (Fioretta Gorini, who isn't even mentioned here but she gave him a son that he unfortunately never saw because he died before his birth)

So yeah, the series absolutely isn't faithful to history about everything, and it does romanticize characters and relationships (all of them, even the friendship between Lorenzo and Francesco Pazzi, that I loved!) to better fit nowadays peoples' sensibilities.. but I don't think they wanted the series to be a documentary, nor I think their novelization of these people is any more ridiculous or invalid than the way countless of other authors had done in their novels before them (including the most praised Strukul). If you criticize this series for that, you might as well not watch any series about historical characters because I can guarantee you few of them, if any, don't romanticize things. Just my two cents.