Neither of these vessels were intended to replace the Iowa class battleships.
And both the Burke and Ticos are far larger than the destroyer and cruiser classes they replaced.
And their replacements are larger still. In fact, the next generation of cruisers are supposed to displace around 14,000 tons. Some 40% larger than the Ticos.
I hate to tell you this, but those ships rendered the
Iowa class obsolete, and what they replaced is irrelevant.

You may think that "bigger is always better", but I hate to break it to you -- it isn't.
Incorrect.
The Ticos and Burkes are air defense ships.
They were not designed for shore bombardment or to sling antiship missiles like the Iowa's brought back into service in the 1980s were used for.
In fact, the Iowas actually had more cruise missile firepower normally carried than either of those class vessels (though it is possible to replace the Standard II SAM missiles aboard those ships with VLS with Tomahawks, but this is rarely done).
And the Iowas were actually brought back into U.S. Navy service AFTER the CG-47 (Ticonderoga) class cruisers began entering service.
Finally, the U.S. Marine Corps (according to Proceedings magazine) has never been happy with the loss of the Iowas given that their fire support for amphibious operations has never been replaced.
When it comes to fire support, missiles cannot replace guns.