How long is a peice of string? Depends what breaks as to how much it'll cost but leaving breakdown aside you'll average about 25-30mpg in mixed usage (Z4 is noticeably more economical than the bigger cars with the same engine) and go through a set of rear tyres about once every 9-12 months @ 320quid a set (Provided you dump the Z4's runflats, tyre size on both cars are the same btw), front tyres every 18-24 months at 220ish a set, and a service about every 9-12 months at 120ish for an oil service, 220ish for an Inspection 1 and 330ish for an Inspection 2. Tax is 240 quid a year or so IIRC.
Once every 2 years you will pay 60 quid for a brake fluid change and once every 4 years you'll pay the same for a coolant change.
The Z4 will cost more to insure as for some reason its Group 19 iirc.
Then its just down to whether anything goes wrong. Roof motor is very common fault on the Z4 - it went on my parents last month, final bill was 800 quid. Looking for cooling system issues as well, budget 500 quid to replace the lot if anything goes wrong as its loads easier. Both cars eat rear coil springs. Also watch out for propshaft centre bearings which can fail at anything from 50k miles. No idea how much thats going to cost to repair, I'll let you know once I've booked the Z4 in
Otherwise they are fundamentally reliable, if the DSC system throws a wobbly its big bill time (I think mine is going to need a steering angle sensor at some point @ 400 quid fitted, it's gone away at the moment but I bet the fault will come back) but this isn't guaranteed to happen, its just a potential.
Keep a grand tucked away for bills and stuff and it'll be fine, IMHO.
The Z4 handles well - better than a 330i because obviously its got quite a bit less weight - but the steering is electric not hydraulic so it lacks the good steering feel of the 330i. This is a shame. The Z4 is obviously a raw car compared to the 330i - the 330i is a better car when its raining, you just want to get home from work, or its freezing cold or whatever. The Z4 is fantastic with the roof down but kinda sucky with the roof up.