I would stay away from both, esp. out of warranty, even with those mileages.  If you want a BMW or any over-engineered German machine then I would only lease.

BMW dealerships do not offer good deals. Ever!

But if you really, really want a BMW, just lease one, drive it, … return it upon lease expiration. Trust me, … that would be the best deal that you ever will get from a BMW dealer!

F.S.

That's actually a pretty good deal for those given they were close to $60K when brand new. With that said, I would not want to own those outside a full bumper to bumper warranty. They're usually pretty trouble free for the first 80K miles or so. If those come with a warranty that lasts until 80K miles or so, or if you can buy one for a reasonable price, then go ahead and get a BMW. But, do not buy it if there's no warranty and if there is, it would be really smart to get rid of the car the instant that warranty expires. 

Broke My Wallet

That is a heck of a lot of money. My reluctance is the previous owners most likely drove them hard. Urge caution. Recommned pricing a new transmission, a couple thousand for repairs and subtract that from the asking price. 

I'd lease or take over a lease on one, or buy a Lexus instead.

I like the 335i. Used to have one. And that is a good price for the year and mileage. 

However, go ahead and add about $5000 to the price as that's what an extended warranty on it will cost, and you want one. Don't buy it without it. Also, neither are reliable. Facts are facts unfortunately, and though they are fun cars to drive they don't hold up well with time and here in the states parts are very, very expensive and maintenance is high dollar as well. Price out the maintenance packs on that car before considering purchasing it.

Leasing new would be the best bet, but you are talking $60k for a new one.