My understanding is that the initial Mini models were made with Peugeot engines, which were underpowered and pretty unreliable. At some point BMW switched Minis over to use a Beemer engine, at which point quality improved dramatically. Mini has been on an upward trend since (as has BMW).

Anecdotally, someone in my family has a Mini with the BMW engine, and it’s been ticking along just fine. Maintenance is expensive though.