A new design using proven systems is one option, usually ignored, that delivers good results.
A split buy of ASW frigates and destroyers, is another option.
Then again, the Burke is no slouch at ASW. If some of the hybrid electric drive options were employed they would be extremely quiet. That is an electric motor on each shaft is driven by the ships generators at low speed, it was a measure to reduce fuel burn on station but could also be tuned for ASW, as the generators are gas turbines installed higher in the hull.
Japan and South Korea have both developed substantially improved Burke's.
This lack of choice is, imho, a result of the US concurrency debacle, which has caused a quarter century of failed US naval and air hardware outcomes. This has lead to less options available to choose from, less design advancement. Even though Japan and SK have nicely adapted the AB, it's still a 1980's design. You can't turn a 1990's Nokia mobile phone into a 2020's smartphone. This has forced us to look at Europe and others for designs, and their offerings are often not optimal given their much smaller defence budgets. Result? Only 1 choice for modern jets. No options for modern frigates or destroyers from the US. Constellation is just a longer FREMM, which we judged not worthy. So here we are.