First visit the following websites for difference you will feel in speed and tyre size:
Tire size calculator
Visual Tyre Size Calculator | Kouki Tech
You may feel extra hardness on uneven roads, resulting extra pressure on axle. Moreover, fuel economy might also decrease.
However, there should not be any major issue. Road grip will increase ( depending upon tyre size e.g. 185/65/r15 or 195/65/r15 have better road grip than stock size in Honda City i.e. 165/80/r13)
Please share you tyre size and brand name. I am also planning to change the rims in my City 2005 to 195/65/R15. Have you feel that rear tyres touched the body with 5 passengers, on sudden jumps?