I was deciding between the two cars, and rented both (well, an Exige was the closest I could find to an Elise for rent) to live with them for a few days. They're both great, but very different. I got an Elise.
Like others have said, you should drive them both, but I'll add that you should drive both a lot, at least a full day, and maybe a few examples of them. Each car might have bothersome quirks, but they could be specific to one example (my Elise has no rattles, though the Exige rental did). I noticed things after a while that didn't catch my attention on the first drive. You might change you mind after driving for a full day or more.
A few details I observed that you might think about when you're test driving:
- Visibility: poor visibility bugs me and I found the Elise better for me. The Exige had none out the back, the Evora had a little bit, and the Elise had a bit more.
- Sensation of speed: wind in my face makes me feel like I'm going faster, and I wasn't getting enough to suit my taste in the Evora, even with the windows down. Roof-off Elise was the winner.
- Knick knacks: where to put our drinks, phones, etc. This stuff can be changed with aftermarket accessories, but in stock form, neither were great for me. Bring your knick knacks along for the test drives, the two cars have different layouts and possibilities. I also measured for my large gear/luggage and was satisfied with both, but...
- Your other cars: I can fit my skiis, and maybe even a passenger into an Evora. I can only get my shorter snowboard into the Elise. That means solo trips for late spring ski days. But we've got a practical 2nd car for winter and trips together, so the Evora's functionality was redundant for me. What else is in your garage makes a difference.
- Ergonomics: the 2 Evoras I drove were ok for me, but the Elise fit my body better somehow, even with its lack of adjustments. Time in the seat showed these ergonomic issues. Bring your usual passenger for test drives too. Mine could not attend with me, and doesn't like the seat as much as the Evora's now.
- Heat: cabin warmth didn't bother me in the Exige and Elise, but the Evora rear window was radiating heat after a long drive and competing with the AC. Might have been a broken window seal though.
- Footwell: I think there is a tiny dead pedal you can add on to the series 1 Evora, but otherwise I found my left foot sitting oddly on the floor. The footwell felt more comfortable in the Elise for me, and had a dead pedal already. But on track the Exige side sill dug into my leg a bit. I heard the series 2 Evora footwell is improved.
- Punishment for driver errors: the Evora gave me the impression that it would forgive lousy driver inputs more than the Elise. Probably the stability control, or lack thereof on the Elise. This didn't bother me, but something to think about.
- QC: I noticed little fit and finish issues after spending more time with the cars. This bothers some people who are accustomed to paying a luxury car price and getting a luxury car in exchange. This didn't bother me, but my wife thinks my priorities are odd sometimes. The newer cars generally sound like they've had incremental improvements.