D.C.
Hello!
Both brands are decent, my son prefers the BreastFlow to the Adiri, as do I. The Adiri bottles are hard to close, if you don't get the lid on all the way, it's an instant leak. While the nipple is very breast-like, the flow choked my son.
The BreastFlow has a two piece nipple that requires both suction and compression which mimics breastfeeding, while most bottles just require compression. The only issue is that the BreastFlow bottles do contain BPA, although the nipples don't, so you have to either hand wash the bottles, or use the Advent Tempo drop-ins if you plan to wash the bottles in the dishwasher.
Best of Luck!
D.