The two series have a great deal in common, and thus understandably there is a healthy amount of debate about how they compare. When it comes to the nature of magic, however, Black Clover is the clear winner. This is not to say that Black Clover is the better series overall; its markedly less compelling villains and the divisive reaction to its protagonist Asta (especially his voice) are evidence to the contrary. But where magic is concerned, Tabata has created a more dynamic and importantly, sustainable, system.
Mashima and Tabata's approaches to magic are similar more often than they are different, and a proper comparison must first address this truth. In fact, it may be more accurate to say that Tabata took what worked about Mashima's concept of magic and codified it further. The primary difference between the two series' concepts of magic is in two key areas: how magic is learned, and the extent to which a type of magic is attached to its user.
It's implied that much of the magic in Fairy Tail is that it can ostensibly be learned by anyone with enough magic power. Lucy, Gray, and all the Dragon Slayers in the series are known to have learned their respective magic, or at least the root of it, from other users of that same magic. On one hand, the transferability of magic in Fairy Tail gives Mashima's characters more freedom than their counterparts in Black Clover, but in several cases it also makes the magic they use feel less unique. This is especially true in the case of Lucy, whose Celestial Spirit magic is based entirely on the keys she carries, along with the fact that she obtained many of those keys (and the spirits attached to them) from other Celestial Wizards.
It's clear that Tabata wanted Black Clovers' characters to have magic that was theirs and theirs alone, inexorably tied to their very identity. His mechanism for achieving this is embodied in two concepts: grimoires and magic attributes. The former is especially important. Grimoires are books of spells that users receive on or after their fifteenth birthday, and contain magic spells that only they can use. They grow with their users, being mostly empty at first and granting access to new spells as the user grows.
The magic attributes in Black Clover include fire, water, wind, and earth, as well as rarer types such as light and darkness magic. Each mage is born with a given attribute and can only use magic from that attribute. In short terms, this means that mages in Black Clover may have the same magic attribute, such as fire or water magic in the case of the Vermillion and Silva families, while each individual's spells from that attribute are exclusive to their grimoire. Together, these two concepts create a feeling that each character is indispensable. This is further compounded by the fact that a mage's grimoire disappears upon their death, and subsequently all the spells they learned.
It's entirely fair to say that Fairy Tail is a better series than Black Clover overall, or vise-versa. The former's pacing is superior, and its world is more colorful and idiosyncratic than Black Clover's, which hews far more closely to a typical Medieval Fantasy setting. For those that prefer anime to manga, Black Clover's animation (at least at its best) puts Fairy Tail's to shame, while Mashima's artwork shines through better in black and white than Tabata's. When it comes to the characters, it's a solid tie.
Where Black Clover really excels is in its magic. The refined two-tier system Tabata created makes the abilities used by his characters feel more like extensions of their personality than tools that they learned to use. New spells feel more attached to a characters' growth and the adversity they face, and this makes such improvement feel well-earned. Additionally, Tabata does more than Mashima to explore the consequences of a magic-centric society, making discrimination and hierarchies based on magic a central theme of the overall story, something Fairy Tail conspicuously skirts around. Black Clover also takes far more time and effort to explore the limits and inherently broken powers of anti-magic in Asta than Fairy Tail did with its resident anti-magic user, Yuka of Lamia Scale. That said, it would be foolish to think that Black Clover doesn't owe at least part of the credit for its comprehensive magic system to the series that came before it, Fairy Tail being chief among them.