Do not buy any BMW.

Please don't respond with a neither one answer.

I'm sorry to say my friend but buying any modern BMW with over 100k miles is going to become a money pit. Plus, one of friends is a BMW mechanic who knows the BMW 3 series that you mentioned and I can say this right now, he told me that they are no fun to work on when they break.

When even shop owner and Master Mechanic The Car Wizard refuses to work on BMWs (and sends them over to his friend’s shop) that should tell you something.

Avoid both - both will be money pits and a labor of love.  Hopefully, you are able to do almost all the work yourself if you plan to buy and also know where to get parts.  Otherwise, forget it!

Well you're asking the equivalent if a person wants to be killed by a knife or a gun. Both would be terrible. I would choose the one with lower mileage every thing else being the same.

Please don't respond with a neither one answer

Well... maybe you can bring down the price of the 100k mile one...

Get it looked over by someone who understands BMWs.

160k miles on a BMW is too much, as an everyday driver it's a bad idea anyway - but, AS I SEE IT, with that kind of milage you can't even really have fun with it.

Just please be ready to spend the kind of money that a 14 year old 100k mile BMW requires.

(I've seen even $5k Mini Coopers require over their price in repairs at 6-7 years of age and 100k miles and that's with a reasonably cheap and simple PSA prince - a car with a direct injection twin turbo 6 cylinder probably will be wayyy more expensive to keep running)

Either one. They are both bad decisions.

Lease a new one instead. Believe me, you will loose less money and enjoy more. 

$9,000 for a 14 year old BMW with 100k I would never pay, personally. That car was $41,000 brand new.  

Old BMWs, and I mean old, talking E28 5-Series from the 1980s and before, are the BMWs to buy. They are easy to work on, for the most part, but they still had BMW electrical issues. A family friend who's now passed had to replace the computer in her '86 528e, and the car only had 40k miles on it 17 years ago. I was 14 at the time and she said she'd will it to me. She wasn't able to. She bought that car brand new and it lived in the garage. There's minimal amounts of their now-infamous plastic crap under the hood, so accidentally breaking stuff isn't likely. You'd be insane to DD a BMW that old.

The E34 from the early 90s is probably the last decently reliable BMW when equipped with the 2.5L straight six and a standard transmission. They have the classic BMW appearance with glass headlights, which I prefer. But again, you're talking near 30-year-old BMWs. BMWs are expensive, no cheap way around it. Buy one somebody just sank a bunch of money into for major stuff and want rid of it, then get rid of it when it starts acting up again. 

The only BMW I'd even remotely consider buying is an old TII, just for fun.

I wouldn’t get a BMW. I had a 2007 BMW X5 from 2016-2020, from 160k-200k.  Amazing vehicle.

But, I spent more money maintaining that thing in 4 years, than 20+ years maintaining my 1999 Honda Accord.

With that said, assuming both check out for the moment, I would get the higher mileage cheaper one, because you will be spending at least $4500 in repairs/maintenance either way.

So think of it as a $9000 for the higher mileage BMW, or $13500 for the lower mileage BMW.

While I too would recommend neither, I am going to assume that as a convertible this is going to be more of a toy rather than a daily driver and that you are already aware that there will be upkeep expenses.

So that said, the one with 160K miles is probably the better value in comparison to blue book values, but 60K more miles is a lot. So I would spend the extra for the one with less miles.

Here's another question you should consider:

Do you want an endless money pit vehicle?

You shouldn't buy BMWs because they are so many things that can go wrong with a BMW. If you really want one as a weekend toy, I would either lease one or try to reduce the 100k mile BMW's price.