I'd say that MajesticSEO still has the biggest database, but it's split between their 'historical' and 'fresh' indices and much of the historical index is out of date. If you have the ability to re-check and process the results yourself then Majestic is still ahead of AHREFs IMO. Their new 'topical trust flow' is quite fun too.
AHREFs has really improved over the last year. I'd say it's almost a match for MajesticSEO in terms of index size; it's smaller but contains less out of date info The main advantage is the interface, they have partial anchor text reports and mostly you can use their reports without too much re-checking.
So if you want to build a top-notch SEO tool based on the API, then MajesticSEO is still probably your best bet (as long as you don't let users see it which requires some negotiation). But if you just want to look at the reports without having to do the work, AHREFs wins.
Unfortunately the other services (MozPro/OSE, SearchMetrics, Sistrix, Blekko, Exalead) are not even close.