Lucca - inside the walls - is small town of ~9,000 with much of old medieval architecture in place with small winding streets and very little car traffic. It has more shopping and good restaurants than a town of this size should because it is the center of the larger 90,000 inhabitant city area that surrounds it. In December Lucca should be relatively quiet, I believe, except for maybe Xmas shopping. Piazza Anfiteatro is touristy but Soto Soto has the respect of the locals if you want to eat there. Otherwise check one of the many restaurant guides to the town - as mentioned Gigi’s is always great.
Arezzo feels like more a city than Lucca with the new part around the train station which slowly filters into the old section as you head uphill. Arezzo is less touristy has many good restaurants that serve local food and places to explore. It should be noted that Arezzo goes all out for Xmas and in December the main square is a huge faire with projected lights at night. I don't know whether this is a plus or a minus for you but it will affect your visit one way or another.
https://rhiz.org/en/arezzo-christmas-markets/
Lucca will probably have some level of Xmas faire stuff but Arezzo is famous for going all out. It's a little early to check the events for Lucca but there are several good websites out there that will list the events going on there.
Have a great trip,
=Tod