Both are excellent pokémon, @ghostflannel, and I admit it will be a difficult choice between the two.

Nonetheless, allow me to begin with aggron. In terms of pros, aggron is partially steel and thus resistant to a higher number of pokémon types, including three out of the four specialties of the Elite Four (if we consider one of Agatha’s specialties to be Poison and Lorelei’s to be Ice). Furthermore, if your child is quite literally halfway through their gym challenge, aggron aren’t weak to Erika’s grass-types (although they aren’t resistant to them either), and they’re positively assets in Koga’s gym. Additionally, aggron generally have tamer personalities than tyranitar, as they’re only territorial, not outright aggressive. 

On the other hand, they’re also generally weaker and slower than tyranitar (except when it comes to physical defenses), and because they’re part-steel, they may also be harder to maintain on a daily basis (as you will need to polish their armor regularly to prevent spotting or rust).

Tyranitar, on the other hand, are far stronger than aggron, and their typing renders them weaker to more elements than a steel/rock-type would be. On the other hand, a tyranitar’s dark typing allows it to be resistant to a different array of types than aggron, some of which may make tyranitar more vital to the latter half of a Kanto gym challenge. For example, whereas aggron is not resistant to psychic-types, tyranitar is perfectly immune to them, rendering Sabrina (one of the more formidable gym leaders) essentially harmless. Likewise, whereas aggron is critically weak to ground-types, tyranitar, while weak as well, won’t be crippled by them, allowing one to handle the Viridian Gym (when it uses its ground-type team, anyway). Tyranitar is additionally resistant to ghost-types and fire-types, allowing it to handle Agatha and Blaine far better than aggron would.

On the other hand, tyranitar and its preevolutions still possess a weakness to more types than aggron does, including grass, but then again, if you challenge Erika, it’s unlikely you’ll be using a rock-type anyway, so perhaps this isn’t much of a problem. What is much of a problem, however, is the fact that tyranitar’s personality make the species difficult to train. They’re naturally aggressive and are very liable to, well, rampage. They are, after all, considered to be the gyarados of the land, and with the sort of power they possess, this can often lead to catastrophic damage. However, it’s also true that with enough patience, a trainer may be able to tame a tyranitar (in much the same way a gyarados can be tamed), so if your child is a particularly patient individual, consider this to be more of a warning than a con.

In short, aggron are more docile and possess better defenses but are all-around weaker and will be less of an asset in the Kanto gyms, whereas tyranitar are dreadfully strong but extremely difficult to handle.

Best of luck on whatever you and your child choose!