Honda Shine is a 125 CC bike. I did a test drive of Bajaj Discover 125 DTSi and Honda Shine. Honda Shine felt better in terms of ride comfort, handling, engine smoothness and gear shift comfort.
But by test riding one cannot judge the mileage. But what I hear from most of the people is Bajaj Discover mileage is better. But still many of my close friends who use Bajaj Discover complaint that the mileage reduces after a few months. I checked with the Bajaj dealer and he accepts the same but not in a straight forward way.
Bajaj's engine and transmission (gear box) were never reliable, on comparison with HH, Honda or TVS. Besides this the success rate of Bajaj Discover is very less - means if 100 bikes are sold most of the customers come back with problems. If you are a fan of Bajaj like many others, better go for Pulsar. To my knowledge that is the only bike that is good from Bajaj. If you believe in quality and durability better go for TVS or Honda bikes. HH is good but too pricey. For e.g., Splendor+ does not have any of the good features provided by other companies, but still it's cost is very high on comparing other 100cc bikes. Glamour FI is not worth the extra money you need to shell for FI.
You can read reports of Honda Shine and other bikes in indiabike.com, overdrive website etc.
Technically speaking Honda Shine engine has very good low end torque, which means you shall drive at speeds as low as 20 kmph on the 4th gear. This implies you need not gear shift often in heavy traffic. Shine also has good high end torque and hence th pick up is also very good (6 secs to 60 kmph).
Hence I would suggest that you shall go ahead and buy a Honda Shine.