here is WHY there is a difference. Grower is meant to do just that... Supply nutrients to help promote growth. Chickens will grow slightly faster and put on slightly more weight when fed a higher protein. Unfortunately, protein is rather expensive to buy for the supplier, so it will cost more. Layer feed is meant to help support a hen to lay eggs as well as possible. There is a significantly higher level of calcium (which can cause problems with growth in chicks, hence why you see lower levels in grower). Protein is not as important to an egg layer, so in order to cut costs, there is less protein. You might also notice that layer is generally less expensive then grower, making it more economical for people who keep chickens primarily for eggs.
Now, saying that, I do find that even my girls do much better on a higher protein feed, so if you feel your girls are not quite as healthy or active looking, your not crazy or imagining it. You have couple of options to look at. You could stay with the layer and try and supplement with extra food to up the protein. (eggs, meat, bugs, certain plants). Personally, this is the least attractive to me because you really run a risk of coming up with a very unbalanced diet. I would suggest on of the other two options, both of which would be much better if you also supply calcium on the side for the hens to eat from if they so chose. You can buy layer feed and mix it with grower. This would be a lower cost then the third option, but not the full protein as previously. The third option is go back to straight grower. Calcium on the side is really necessary here and this option will cost the most.
Only on a personal option, i chose the second option, but instead of using grower, i use a game bird feed, that is 23% protein (here it only runs $.50 more a bag and allows me to use less to up my protein to 19%, which is where my girls thrive). It ends up being the most cost effective way for me to reach a level of protein that is best for my girls while keeping costs down.