The 260E will have a better performance given it has the bigger engine... and has more space.

The 316 should be more nimble through the corners as its a sport sedan and friendlier on the fuel budget.

It's hard to compare the two directly as they are of different vehicle classes and variants. What one has, the other doesnt so you have to look and see what you prioritize more.

At a 350K budget you'll be hard pressed IMO as you will expect repairs to be done on any of the two. A 316i at 350K may not also be in tip top condition.

Another Euro car you can get for 250-300K is a 2000 to 2001 Opel Astra.