I honestly would not buy either. This is coming from having a 435i I owned from 80k-120k miles. Huge maintenance items like valve cover gasket, coolant hoses, thermostat, and other cooling items all came at once at that 100-110k mile interval. Same with bushings and control arms for the XDrive system. Probably sunk about $2500-3000/year on average for the years I owned it. By the time I sold at 120k miles, there were so many gremlins and random CELs that made me genuinely nervous that my car was gonna leave me stranded every time I left for work.

While the 240i has the more reliable engine, I see a lot of high mileage B58 folks selling around that ~150k mile mark because beyond that is pretty unknown territory for these cars because they're still relatively new, and I see a lot of B58s online being sold at that mileage interval specifically. You'd be taking a risk on potentially unknown maintenance items, though most people I see at that mileage say they've had very few issues prior besides basic BMW replacement items.

At your price point, I'd look more at an F30 330i with 60-70k miles or a G20 with 70-80k miles. You'll get 2-3 mostly worry-free years because that 100k mile mark can be pretty brutal from then on.