Hands down, the easiest merchant processor to integrate into Gravity Forms or WooCommerce - I have to imagine it integrates just as easy with other popular tools, but my experience is limited to Gravity Forms and WooCommerce. Within Stripe itself, navigating is intuitive and easy with very friendly report tools. Looking up transactions is easy and may be search by name, email address, transaction id, and even partial data (like billing address, product, etc). Full and partial refunds are also very easy to manage.
The reporting is especially helpful as it goes back in detail for as long as you've been a customer (so, I have data going back 3 years all readily available). I also appreciate the popularity of Stripe and how common third-party integration has become - in my case into AgileCRM and Freshbooks.
Lastly, they have an amazing free iPhone app. Very useful for when you're on the road and you can basically do everything from the app that you could do from their desktop dashboard.
I have never won a dispute - no not one - and the process seems entirely automated. While I have only had four disputes in the past 12 months, all of which were admitted mistakes on the customer's part, I submitted emailed conversations with the client where they admitted error, and I still lost. Since then, I've been told it's best to get the client to contact their credit card company to rescind the dispute but it was frustrating that the process is so automated that it seems not to favor the merchant.
So, with that in mind, if you ever have a dispute, work with the customer to get them to rescind it.