Next to Majestic SEO, Ahrefs.com is probably the main tool specialized in backlinks. In comparisons, both go side to side when it comes to discovering links. WebCEO is using Ahrefs as the backlink data supplier in their website analysis tools. Ahrefs is very good at spotting new and lost backlinks and also offers some additional options, like on-page SEO metrics of metadata, H1 tags, response codes, pagespeed, compression, etc. A free account is allowed 3 of these on-site reports per month, which should give you an idea of the possibilities.
Most important part of the service is of course the extensive list of backlinks that can be aquired, all in nice reports, and all downloadable. This is the heart of the application:
Ahrefs provides a very nice interface, with lots of nice graphics, like this example for a view on links acquired for Joomlaseo.com over time:
This can also be broken down in stuff like referring domains:
Before buying a subscription, I would advise you to try the free account. Paid subscriptions start at $79,-, which should be fine for a smaller agency.