I agree with Marcelo, "with more facility" sounds more academical, more "bookish" than "more easily than".
I found some sentences with "facility" and they confirm (or almost) that:
Seeds are carried with more facility when provided with plumes or wings.
On the whole they are mild and easy-going and even apathetic, but the facility with which they learn is remarkable.
He became a good classical scholar, and learnt to speak and write in French with facility and elegance.
It may be asked whether straight lines cannot be traced by the hands or feet with more facility than curves.The gases quit it
(speaking of stomach/reflux etc) with more facility than the liquids, and these more easily than solid food.
(From Google Books - An Elementary Compendium of Physiology) This one with more facility than
, plus more easily than
- indeed an ingenuous way not to repeat the same sentence! So, it means one and the same here...
Seeing Google Ngrams, one sees that the use of "ease" compared to "facility", "ease" wins hands down. All the time.
Not that I am advocating that Ngrams is some panacea or silver bullet when it comes to English study, many wouldn´t use it to draw conclusions:http://www.wired.com/2015/10/pitfalls-o ... gle-ngram/
But such difference really makes one think!