I've had my GT86 for about 6 months now and sold my S2 111S Elise a couple weeks ago after 4 years of ownership. With a little one now the Elise was hardly being used and since I got the GT86 I think I went out in the Elise a couple times.
They have similarities, great handling, an engine that needs to be worked to get the performance and they feel similar to drive in that the GT86 feels racey like a sports car. Ultimately an Elise is faster, handles better, stops quicker but its very hard to reach its limits on public roads so is best reserved for track not to mention the compromise in comfort and practicality.
For day to day the GT86 is great as its easy to have fun at legal speeds, its not that slow either, A-B it makes good progress.