Monster Rancher largely exists to promote the video game series that it's based on and is pretty by-the-numbers as far as plotting and characters go. It actually consists of two separate TV anime that were aired for it in Japan and aired in America in an edited format to appeal to younger audiences with Western sensitivities. While largely having the same cast of characters between both seasons, both seasons are quite different in mood and premise with grade-schooler Genki Sakura whisked into the video game of the series to aid teenage Holly and several other monsters with stopping evil monster threats.
The first series features the main group trying to locate the Phoenix, a mythical monster with the power to oppose the threat of the villainous Moo. This series has a more serious mood depicted as monsters are shown to die at varying points of the series when dealing with Moo and his minions, and Moo is depicted as a menacing and merciless enemy threat when Genki and his allies have to contend with his forces.
The second series plays out more as a tourney-style monster battle competition a la Pocket Monsters as Genki and his friends have to compete in monster-battling tournaments to win championships toward winning a prize that contains the magic stone that was used by Holly in the previous series to try locating the Phoenix. This series is noticeably more lighter in mood compared to the first one as no monsters or humans are shown to die throughout its run and there is a bit more emphasis on humor and competition compared to the more serious stakes of the first series.
While I do get that both Monster Rancher anime were made in mind for younger audiences for their target audience, it doesn't necessarily make it a memorable anime in the same vain that anime fans would get from their viewing of more popular titles aimed for children like Pokemon, Digimon, and even Dragon Ball Z. Unlike those three titles, Monster Rancher doesn't have anything in particular that strongly sticks out with it to attract a wide audience. The characters are largely two-dimensional character types, the plot developments being pretty one-note with events, little to offer in the way of world building, and way too much dependency on Power of Friendship plot devices for the heroic characters to get by in battles. In essence, the two Monster Rancher anime largely try to ride on the video game franchise's name recognition to try drawing an audience while doing little to add any substance to it to make it more engaging.
If you are looking for any anime series for your children to be drawn to that are based on popular video games, I'd strongly recommend keeping away from the Monster Rancher anime and just have them stick with anything like Pokemon and Digimon that have more to offer in engaging their interest.
