I guess it depends on what you mean by “custom dictionaries”. You can definitely download dictionaries from the Kindle store and then set them as your preferred dictionary in the iOS Kindle app. When you select a word there is a dictionary pop-up where you can choose the active dictionary from the drop-down menu. I downloaded a free dictionary to test it out, but there are also paid options. The built-in J-J dictionary is 大辞泉.
I used to use ebookjapan, but I have since switched to Kindle for books. There were severe limitations to highlighting in ebookjapan (I think like 10 highlights per book), while as far as I can tell there is no limit in Kindle. I like to highlight things to discuss in the threads or read-aloud for book clubs (although I frequently forget to do so). If you are only reading manga I don’t think you will see much of a difference. Both services have similar sales and rewards systems. I haven’t noticed a significant difference in image quality for manga. Books have adjustable fonts, so there’s no need to be worried about image quality for those (unless there are pictures).
The major downside to Kindle is that you have to switch accounts if you have a Kindle account in another country. Switching accounts deletes all of your downloads, so you would have to re-download your purchases every time you switch accounts. You could solve this problem by having a second device that you use for one of the accounts, but that obviously has an increased cost associated with it.