Baumalu cookware is a pretty good line of copper, and is generally favorably priced compared to Mauviel or some of the others. Tin lined cookware is generally accepted as being superior in cooking quality to SS lined, but does have some drawbacks. Notably it scratches easily and must be used with wood or plastic utensils. For this reason, I would not recommend tin lined cookware in situations where there are a multitude of users. Retinning is not nearly the problem as some make it to be, but it is expensive. $5.00 per running inch, diameter + height plus shipping at present. Daily use pans should last years with proper care. SS is the better choice if it is not going to get the proper care. Baumalu is tin lined, and seems to be thinner than some other in lined pots. I am assumung you are talking of SS lined Mauviel, although they do make tin lined pans.
Baumalu is the better priced of your choices. Get the 2 mm with no rolled edge. The rolled is a thinner copper. Mauviel has long been considered as among the best. Cast iron handles perform better than brass. Mauviel's CI handles are heavier than Baulmalu
Worthy of consideration is a set of 4 tin lined saucepans with 3 mm thickness that are available at Rocky Mountain Retinning. Peter bought the parts and assembles and tins them on premises. The last I talked to him, he had only a very few sets left. These are top quality with hammered exteriors and heady cast iron handles. With lids, the price is $345. I have purchased 2 sets.
Bottom line. For me, Mauviel feels better than Baulmalu, but I prefer tin to SS. If you have kids using the pans, I would recommend SS. Baulmalu is the better priced and is sometimes priced at low sales prices. Either brand will work well.