Puglia or Sardinia for family trip?

Have you seen this recent detailed trip report, covering Puglia as well as some other parts of southern Italy?

https://community.ricksteves.com/travel-forum/trip-reports/trip-report-bella-puglia-plus-basilicata-and-rome

I’ve been to both but safety shouldn’t be the deciding factor. Why shouldn’t they be both safe?
The deciding factor should be your personal preference. Sardinia is primarily a beach/scuba diving paradise. There is also some stuff of historical importance but probably not as much as the mainland. Sardinia is mostly about nature, in particular jaw dropping turquoise sea.
Puglia has some of that, particularly the Gargano and the Salento, but there are more historical sights to see, including Matera which is not technically in Puglia but near.
So it depends on the type of vacation you want.

Sardinia hands down. The culture there is so different and the good food and Cannanau wine. Make sure you do a bunch of the Agritourismo places to eat. Like a 12 course meal for $30 euro.

What does your family consist of (ages, etc.) and what kinds of things do you like to do and want to do?
I would find intensive sight seeing in Sardinia difficult with children, for example, due to the need to drive to the interior.
OTOH, it is reputed to have amazing beaches.
Puglia has many sights that I think might interest children (the trulli, caves).

Thanks for the info! Two daughters, ages 6 and 9. We enjoy slower pace, they love the beach and animals. We'll visit Rome and Florence, I was thinking Sardinia could help balance. We have 23 nights in late June and July to spend in Italy. We are still trying to plan the tail end of the trip, which will end in Venice.

I imagine the same is true of Sardinia, but Puglia can be oppressively hot in mid-summer. Strike that: will almost certainly be oppressively hot in summer. I loved it, but with young children be sure you build in many, many beach or pool breaks, and place a premium on hotel locations that permit a quick retreat for a cool afternoon siesta.

Some of the towns are full of whitewashed buildings, so don't forget sunscreen on faces even though you'll (I hope!) be wearing broad-brimmed hats.