If you have a fancy sports car, you can feel acceleration. It slams you back in your seat. (check out this: https://secure.wikimedia.org/wikipedia/en/wiki/Equivalence_p...) You cannot however feel speed.

Therefore, you can measure acceleration with nothing but equipment (a simple spring-scale will suffice) in your car (reference frame), but you can only measure your speed relative to something outside of your car (traditionally, the road).