Does the NuvaRing have more side effects than the Pill?

The increased risk for developing blood clots is a very serious side effect deserving of strong consideration. I do not have personal experience or advice to share with you. So, like you, I did some research. This is what I found:

The risk of getting blood clots may be greater with the type of progestin in NuvaRing than with some other progestins in certain low-dose birth control pills. It is unknown if the risk of blood clots is different with NuvaRing use than with the use of certain birth control pills.
So, depending on which birth control pill is prescribed, the risk for developing blood clots may be equal.

Taking hormones can increase your risk of blood clots, stroke, or heart attack, especially if you smoke and are older than 35.
If any of these apply to you, then I would not consider using NuvaRing.

Do not use NuvaRing if you have any of the following conditions: a history of stroke or blood clot, circulation problems (especially if caused by diabetes), a hormone-related cancer such as breast or uterine cancer, abnormal vaginal bleeding, liver disease or liver cancer, severe high blood pressure, severe migraine headaches, a heart valve disorder, or a history of jaundice caused by birth control pills.
Again, if any of these conditions apply to use, do not consider it an option.

Ultimately, the decision is yours. Comparing all the pros and cons can help you choose the right form of birth control.
Maryann