This is an interesting thread for me, because I made a similar move. I have owned two TTS's (with a gap between), the first one manual, the second was an auto. All I have to say is the Evora is in a different league altogether. Obviously the RS has more power than the S, but other than that they're very similar cars. So that you're aware, I've gone from a Mk2 TTS to an S1 NA Evora.
While I owned the TT's I always felt like they were a good compromise between a practical car and a sports car - they had a surprising amount of room in the boot, were pretty comfortable and were quicker than most things on the road. The problem was, I always felt they were a bit emotionless - the four wheel drive makes it fun to just plant your foot mid corner and get dragged out of it, but ultimately I always felt like the car was doing most of the work for me. Being a turbocharged engine there was plenty of torque when on boost, but it faded massively towards the redline, and I ended up getting a bit bored of the lack of excitement at the top end. It was actually when I bought my motorbike that I started craving a naturally aspirated car again, that feeling of it pulling all the way to the limiter is so much more exciting than low down torque in my opinion. I still like the TT, but I don't miss it. Evo magazine described the TT as "effective rather than exciting" which I agree with - it'll go quickly, but you don't feel that involved. Anyway, here's my thoughts on the two.
Where the Evora wins:
Steering: As soon as I drove the Evora my eyes were opened. The amount of steering feel was one of the first things I noticed - with the TT you turned the wheel and knew roughly what the wheels were doing, but you couldn't really feel anything through them. The Evora has a much sharper rack, and you get a whole lot more feedback when driving.
Suspension and chassis: The TTS had adaptive ride, which initially I loved, but have since come to despise in modern cars. The normal mode was fine, sport mode killed body roll but was far too hard for British roads so rarely got used. Lotus have a different way of doing it - rather than just make the suspension ridiculously stiff so you don't get body roll, they allow a bit of roll so you can feel what the car is doing, and also have a reasonable amount of comfort. Turning into corners you feel like you have so much control over the car. The TTS had good traction, but ultimately wasn't controllable in the corner - if you went in too fast it just understeered, the Evora on the other hand is beautifully balanced and gives so much confidence. A lot of people on here say that the Evora rides better than an executive saloon etc, but I'd have to disagree there - maybe my car is firmer than theirs or something, but the Evora definitely has a pretty firm ride. That's not a criticism - a sports car should have sports suspension, and while it's been fine for all of the journeys I've done, don't expect a Rolls Royce.
Engine: As I mentioned earlier, this was always a bugbear for me with the TTS - it pulled well at first but didn't have much character, and especially lacked an exciting exhaust note. (It seems the UK is full of 4 cylinder, turbo charged VAG engines which all make that stupid parp as they change gear). This will be less of an issue for you because the 5 cylinder is a much nicer engine both in power and sound, but the Evora 400 still sounds better to me, and will pull to the redline.
Desirability: I like the design of the TT, and still think it looks like a cool car, but the Evora is head and shoulders above it. I didn't buy the car to get looks, but there's no denying that it's a head turner. I got fewer negative comments than I expected when I had the TT - just a couple of 'hairdresser's car' or 'golf in a frock' comments, but on the whole most people quite liked it. On the other hand, the Evora has only had positive comments - people are desperate to sit in it or have a ride, and the only negative comment I've had so far is my mum saying 'it's a bit ugly isn't it', but she never has anything nice to say about my cars, so we can all ignore that. I've taken it to a couple of local car shows, and both times I was asked if I would display it as I went to pull in to the public car park, I definitely wouldn't have got that in the TT.
Where the TT wins:
Practicality: I regularly pick up the weekly shop in the Evora, and have a car seat for my 10 month old son which fits in the back, as well as a pram that fits in the boot, but we were very limited in options when it came to choosing those. In comparison, the TT could easily take my bicycle or snowboard in the boot without any issues.
Build quality: The interior of the TT is really nicely made, I never had any squeaks or rattles and in fact I never had any reliability issues in either of my cars over the 5 years I owned them. In comparison, the Evora makes a lot of noises while on the move, and half the interior is just stuck on with velcro so don't expect the same standard as your RS. Before anyone jumps in with the 'hand built car' comment, I don't have a problem with the noises - the driving experience more than makes up for it, but it definitely needs to be said, they aren't as well put together as most mass-produced premium brands.
All weather usability: To be fair to the Evora, I daily drive it, and have been driving it to work in the snow we are currently experiencing, so this is a bit of an odd one, but being 4 wheel drive, and slightly higher off the ground, the TTS was a more reliable choice in bad weather. I have definitely had to be more careful with the power in the Evora, so although it's not let me down in the bad weather, the TTS is the winner here.
Reliability: Again, this is going to be very subjective to each car, but as mentioned I had two TTS's for a period of 5 years, and they were bulletproof, just required regular maintenance. I've had my Evora for 6 months, and so far have had to replace the AC compressor, AC condenser, radiator and rear lights, and one of the displays on my dashboard doesn't work. It's a 9 year old car, whilst my TT's were around 5 years old while I owned them, so that's worth taking into account. So far the engine in the Evora has been reliable, and I've not been stranded by the side of the road, but it was a close call on one occasion.
Where they draw:
MPG: I get around 25-30mpg on my commute for both cars, not much more needs to be said.
Right, I think I've bored everyone enough now, but to summarise, I absolutely recommend the Evora.