From this, I would say the size does look actual. JS Hyuga and JS Kaga don't use the same sonar. Also, JS Kaga is a considerably bigger vessel, so her sonar will look proportionally smaller. Size comparison of the two classes:
JS Hyuga uses OQQ-21 sonar. JS Kaga uses OQQ-23 sonar. OQQ-21 is similar to (derived from) the US AN/SQQ-89(V)15 sonar.
Japanese language Wiki with info on their sonars:
I cut/pasted the OQQ-21 & 23 sonar info into a Google translation and got these. It should be noted that "Frank array (FA)" is actually "Flank array"...runs along the lower flank of the ship's hull. Japanese has trouble with L's.
"First, the Hyuga type (16 / 18DDH) was equipped with the OQQ-21. As a practical machine based on OQS-XX, it is equipped with a huge cylindrical array (CA) sonar equipped on the bow and a long Frank array (FA) sonar equipped on the bottom of the ship, and also in the United States. Based on the AN / SQQ-89 (V) 15 of the  CA sonar and FA sonar share functions, which makes it possible to secure the required detection performance in various operational environments, from long distances to short distances and from deep sea areas to shallow water areas. In addition, by applying the broadband element technology newly developed (research and trial production from 1997) after the trial production of OQS-XX, it is possible to parallelize the ability to avoid obstacles due to high frequencies as well as low frequencies for long-distance anti-submarine search. succeeded in. In addition, the technology of towed sonar is also applied to the function as a listening device  ."
"The OQQ-23 is mounted on the Izumo type (22DDH), and has a configuration in which only the cylindrical array sonar of the OQQ-22 is omitted, and neither the Frank array sonar nor the towed sonar is omitted. In addition, since the same type does not carry anti-submarine weapons of individual ships, anti-submarine information processing equipment is also omitted. 
So, you can also see that the sonar carried by JS Kaga is a simpler system, which can also contribute to the size difference.