Hormonal birth control pills also vary in their affects on your body. Some brands/versions have higher dosages of the hormones than others, and they all use different formulations (which you or any other individual may respond to differently).
I think it used to be more common for women to take hormonal birth control that had a very high dosage of hormones, because that was what was available (particularly when this form of birth control was new). As more studies have been conducted and the medications themselves have changed, I think there are a lot more low-dose versions of birth control on the market. I've only ever taken pretty low-dose versions, and since they work for me, no doctor has ever suggested I switch to anything with higher doses of hormones.
So personally, I experienced no change. In fact, I experienced no negative side effects at all. The only things that really changed for me were what was supposed to change -- I (mostly) stopped getting cramps, and I stopped having crazy mood swings. Other than that, nothing really changed. I started taking hormonal birth control almost 10 years ago, but the general effect the drug has on me has basically stayed the same.