The BPI is a trade association for all UK record companies, including the majors, whereas AIM operates solely in the interests of the independent sector. Both charge an annual registration fee and a percentage of your PPL income.
BPI: £67.50 + vat + 5% of PPL income
AIM: £125 + vat + 10% of PPL income
Both offer training, education and information seminars, registration discounts and access to travel grants for attending international trade fairs etc. Often members from one organisation can enjoy member level discounts to events organised by the other. The BPI holds regular independent label committee meetings, while AIM runs a number of useful forum events (Music Connected / Indie Con). The Aim website also has a great ebook section with useful guides to running a label, digital and sync, which is free to members.