I have used both of these email marketing services and here's a summary of what I think about each of them.
It has a free plan, which is great for beginners. The interface is simple-to-use and easy-to-understand. It is also adding useful new features at a faster rate than most email marketing services out there. In terms of email deliverability, I am not an expert to comment on the technicalities but I'm satisfied with my open and click rates.
One particular feature that I love most is that you are able to set your email to be sent out at a certain time regardless of time zones. For example, if you have specified your email to be sent out at 9AM on a particular day, the email will reach your users at 9AM in their respective time zones.
If you have an existing email database, you can import it into Mailchimp and start sending emails to your subscribers without having them to verify their subscription again.
However, there is no way to build lists on a campaign basis. For example, you have a main email list for blog readers and another email list for subscribers that signed up for a special ebook. If a subscriber is on both the lists, he or she will get two copies of your broadcast message if you have it sent all your lists. This was the main reason why I switched to AWeber but this may have changed since then.
Getting used to its interface requires a steeper learning curve and it doesn't come with a free plan. I've got no complains about its deliverability and I still get around the same open and click rates as Mailchimp.
It might be a hassle to migrate your email list to AWeber because the importing of subscriber emails will require your subscribers to verify their subscription all over again.
The good thing about AWeber is that it allows me to send a broadcast to multiple lists and duplicated emails will only receive the broadcast once.
Do let me know if you have more questions about the two email marketing services above.