I've used Aweber because "serious marketers" used it. So I paid my $180 a year and jumped in. It is my fault, but I didn't use many of the tools that are there. They have automation tools, but in the end I have a ton of people who have unsubscribed over the years (again, not Aweber's fault). As I don't have a ton of people on my lists, I don't run into problems, but if you are having to pay more because your lists are large, Aweber makes you pay for people who have unsubscribed (but you've never removed - according toe convertkit.com's site). Until recently, you could not add a list to aweber without doing a double opt-in. In some cases (without using the list automation) you could easily have the same person on multiple lists and be paying for them. For me, I've been paing $15 a month ($180/yr) so it did what I wanted it to do - send email, and convert an RSS feed to an email. 
I've wanted to start doing more strategies to build my list. I purchased Lead Pages, and purchased Optin Monster, and when I saw videos on ConvertKit it is part Aweber, part lead pages, part optin monster. The price seems a bit hit at $29 a month for 1000 subscribers (you can send 10X the number of subscribers). But then, if you're paying for unsubscribers it may be cheaper. 
The cool thing is you can EASILY create segments of your list and just send (or exclude) them. I like this idea, especially for those list that I want to do more than send out a follow up email. Check out these videos from Convertkit.
 
Videos at www.weeklywebtools.com/300