I'd use the non-top tier BP fuel without much reservation.
That being said, their stations here are all franchise locations, meaning its like a box of chocolates - some may be nice, some meh, and some terrible. These days, most are already on their way to the terrible status around here. Run down, outdated, etc... (BP, Shell, and Marathon all fit in this category here)
The Amoco name was killed and then resurrected by BP in recent years to offer franchise owners another nameplate and the opportunity to sell gas under different branding when they have locations near each other. It was remarkable when BP decided to kill off a well known brand in the Central US (Amoco) and rebranded to BP...
Lastly, the source of your gasoline is wholly dependent on your geographic location. If its all pipeline sourced, etc... then yes, there is liklely little difference by brand.
In this market, there are two local refineries, and a dedicated brand pipeline - and supply agreements with certain brands. Testing in the past confirms this is the case in this market. Statements about how EPA standards make all gas the same are not exactly correct - they may be the same in terms of meeting the testing requirements, but the ingredients/formulation can be very different.
(For those who are wondering about the sourcing, Speedway gets its gas in this market from the Marathon Saint Paul Park refinery, Holiday from the Flint Hills Pine Bend (Rosemount) refinery, and BP has a dedicated pipeline from Whiting IN to a terminal in the Twin Cities. Historically, BP also owned a refinery in Mandan, ND that has a pipeline to the Twin Cities terminal that receives product from Whiting, but through a series of sales is now a Marathon refinery. Testing has shown very different makeup of regular gas from the three sources)