The answer to this question states that all of the remaining Empire supporters eventually became the First Order, but does not describe how large it is. I'm mostly curious in terms of total members and systems controlled.
At this point, we can only speculate.
However, there is an indication that the First Order is slightly smaller when compared to both the New Republic and the (now disbanded) Galactic Empire. Both quotations are taken from Wookieepedia.
Many within the military believed that despite being outnumbered by the New Republic Starfleet, their technological superiority was so complete that even their smaller navy stood virtually unchallenged
As a result of the incidents leading up to The Force Awakens, it seems that the First Order is numerically smaller in scale than its predecessor.
With the First Order lacking the numerical superiority of the Galactic Empire, better equipped and trained soldiers resulted in higher trooper proficiency than the previous Galactic Empire.
Again, although not specific, we can gather from this that the overall size of the First Order was smaller relative to both the New Republic and the Galactic Empire and that the First Order was, to an extent, measured more by their technological capabilities rather than simply their overall size.
It should be noted that this article compares the First Order to the New Republic. This is not necessarily the same as comparing the First Order to the Resistance.