Found the receiver at top of photo at the Phoenix Gun Show last weekend.  It's a "low serial number" specimen, serial 38XXX, serif numerals, side extractor slot in frame.  I got it home and rummaged through my Favorite part stash, finding everything but a trigger and a barrel screw.  The one below was in the parts stash, another "low number" side extractor version, serial 75XXX, more blocky or "Roman" numbers.  And, of course, the most noticeable difference, the right-angle between barrel housing and receiver on the first and the fillet between the two on the second.

 
So I guess the transition between right-angle receivers and filleted receivers was somewhere between those numbers.  Uscra112 has been compiling lists of Stevens 44 numbers and characteristics and John Boy the 44-1/2s; if anybody is interested in Favorite transitions, here's a couple data points for you.

Look at the top picture, see where the frame has a square cut to the frame where the breech block is, compared to the more round cut to the frame in the bottom photo. Very early model 44’s also have the square cut frames.

I just bought a 44 and haven't yet got it out of my FFL's shop, but the receiver resembles the one in your lower picture and the serial no. is 25XXX.  Where would this fit in the chronology of production?

@Bent Ramrod - Does that one have the two-diameter barrel shank?

Barrel housing?  Are you talking about the receiver ring? 

And what is the "factoid"?

I notice the hammers are different shapes. 

Without digging through my notes where I noted the "serial numbers" of several hundred Favorites over 4+ years before I got bored, I picked up a few examples.  My side plate favorite has s/n 679 stamped on the front of the frame and also the adjacent side plate in tiny letters seen after removing the forend.  Also has a 7 o'clock extractor, slightly curved butt plate, round barrel with 1884 patent date and neither tang is marked.  Has Beech folding front sight and a simple notch rear barrel sight.  This has a large slotted take-down screw.

     Number 4515 is stamped on the lower tang of the next one with English proof marks, 1/2 octagon barrel with the 1994 patent date on the top flat bracketed by a "negative" pair of X's formed by 4 triangular impressions which lasted past the later advent of the 6 o'clock extractor.  It is also threaded for a silencer and has a folding Beech front sight along with target scope blocks and a metal butt plate

S/n A 11085 has the wide 6 o'clock extractor, and the same roll stamp on the top flat of the 1/2 octagon barrel, rounded frame side cut, Black hard rubber Favorite marked butt plate, folding Beech front sight and a full sized Stevens tang sight.  After the A series, serials had a letter or figure  and up to 3 digits, a system that lasted until well into the 1915 guns when high numbers again appeared.   

     Number & (ampersand) 62 has the short-lived barrel tension screw, no "boxed X" on the otherwise same patent marking.  Following this, the serial numbers used some other figures and romped through the alphabet perhaps more than once.  The two diameter barrel breech apparently went out with the 7 o'clock extractor and the square cut-out of the frame somewhat near 1900.  The 1915 versions were somewhat boring to record.     -  James Hays