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The R15 is a track bike primarily, meaning that the riding position, dynamics etc are designed for maximum takeaway on racetracks. Which is not to say that it will not be enjoyable everyday on the roads, just that it may not be very comfortable over long distances in the lean-forward position. But if you are light-weight and flexible, the R15 is a tremendous machine and will give you thrills you expect from fast motorcycling.
The Classic 350 is a different 'kettle of fish' altogether. It's a low rpm, long-stroke, push-rod motor, often called a 'thumper' for obvious reasons. An RE is all about relaxed motorcycling, traveling long distances with ease and enjoying riding for riding's sake. The new UCE motor is really good and I can say that with authority since I ride a new Classic 500. If you can stretch the budget a bit, go for the CL500 eyes shut. It's fuel-injected, faster than the R15, as quick and a much better cruiser. I get a mileage of 30 kmpl and the engine's still not completely run-in.