It is very common that new cars come with bigger wheel, I think 2010 Accord come with 17" rims.
With low profile tires, you will feel "顛簸", but you get better "handling".
Your old Mazda probably has 14" rims, which gives you more comfortable feeling but less handling.
I think this is why you feel 顛簸, if you don't like it, try look for car come with 14" rims... Mini Van usually has smaller wheels.