The Two Farm Systems: It really is a good news, bad news situation for both organizations when it comes to the first base position. The bad news is neither organization has a whole lot of depth of quality long-term first base prospects and the good news is that both organizations already have the position filled for the foreseeable future with Freddie Freeman  and Ike Davis  respectively.
In fact, not only does neither organization have a lot of depth but neither one has a first base prospect with the kind of potential impact anywhere close to the big leagues. The Mets arguably could have the top two best in-house first base options in either Wilmer Flores or Aderlin Rodriguez but, both playing primarily third base right now, neither has moved over to first base permanently yet.
The first base landscape could clearly change if either or both do wind up moving to first base - a move that seems inevitable, especially for Rodriguez, with David Wright locked down at third base for nearly the next decade and considering neither player is a great defender at third. Flores could bring great hitting potential to the position with decent power and Rodriguez could bring great power potential should he move.
For now though this comparison will focus solely on the guys playing first base predominantly at the minor league level. And it's with that parameter where things get pretty shallow for both organizations.
Barring a move of Flores or Rodriguez, the Mets offer very little at the first base position. In fact, without that shuffle it looks very bleak. 28-year old Josh Satin has some great plate discipline and average power, but he's better served as more of a utility player than everyday guy and he's getting a bit old to be still considered a prospect.
New York's Eric Campbell, who will turn 26 years old shortly into the 2013 season, is Double-A tested and like Satin shows big league plate discipline, but his power is more average at best and therefore not a long-term solution at first base. Even the Mets' lower-level first base prospects -- Jayce Boyd and Cole Frenzel -- fit a similar profile as players who should have very good minor league careers, ones who will hit well and show good plate discipline, but whose power is quite limited.
Atlanta is no different at the higher minor league levels either. Yes, Ernesto Mejia has some legitimate big league power potential but his plate discipline is suspect enough that talent evaluators question whether or not he can keep up hitting for a good average at the big league level.
And like Campbell with the Mets, Atlanta's Joey Terdoslavich  and Chris Garcia  both show the requisite plate discipline and patient approach needed to be quality hitters, but neither has the above average to plus power potential needed to man the first base position in an everyday capacity at the big league level.
While the Braves don't have much in the way of upper-level first base prospects, they do have some intriguing guys at the lower levels that provide some interesting long-term ceilings. Left-handed hitting William Beckwith just might have the highest ceiling among the first base prospects in either organization. He just turned 22 years old at the end of the 2012 season, a year in which he hit .291 with 15 home runs for the low-A Rome Braves. He has a lot of power potential and he has shown he can hit, but at 6-foot-2 and a modestly listed 220 pounds [he's probably more like 250], conditioning could be a long-term issue with him.
Another intriguing 'what if' candidate for the Braves is Brandon Drury, the 2011 Appalachian League MVP. He took a big step backwards in 2012, however, hitting just .229 for low-A Rome, but the former third baseman seems much more comfortable at first base and he just turned 20 years old at the end of the season last year so he still has plenty of time to tap what is a pretty high ceiling.
Soon to be 20-year old Robinson Arno is another long-term project that could pay dividends but he's far from a legitimate prospect right now. At 6-foot-4 and 225 pounds, he has a nice combination of size and projectability, but his approach needs work offensively to become a better overall hitter and make better use of his above average power potential. He's looking more like a long-term Mejia type at this point than a viable big league possibility.
How Do They Compare In...
Power: Atlanta has just a bit too much depth power-wise at the first base position right now with Mejia at Triple-A, the combination of Beckwith and Drury in A-ball, and Arno as a high-risk, high reward slugger. Things would change quickly, however, if either Wilmer Flores or Aderlin Rodriguez moves over to first base full-time, but for now the Braves have a bit too much here. Advantage: Braves
Hitting For Average: While Atlanta has some slugging types, New York has a few too many quality hitters for average at first base right now and that would be doubly the case if Flores were to move over. Advantage: Mets
Defense: This is really a toss-up category as there really isn't one standout defensive first baseman in either organization among the legit first base prospects. Drury is young enough, athletic enough, and inexperienced enough to push this in Atlanta's favor at some point but he needs to prove it first. Advantage: Even
Overall Potential: Until either Flores or Rodriguez, whose massive power potential is undeniable, move to first base, both of whom would climb right to the top of these rankings, the better stable of young first base prospects reside on Atlanta's side for now. Advantage: Braves
Highest Ceilings: William Beckwith (Braves), Brandon Drury (Braves), Robinson Arno (Braves), Chris Garcia (Braves), Joey Terdoslavich (Braves)
Best Power: Ernesto Mejia (Braves), William Beckwith (Braves), Robinson Arno (Braves), Brandon Drury (Braves), Josh Satin (Mets)
Best Average: Chris Garcia (Braves), Josh Satin (Mets), Jayce Boyd (Mets), William Beckwith (Braves), Joey Terdoslavich (Braves)
Best Defense: Joey Terdoslavich (Braves), William Beckwith (Braves), Brandon Drury (Braves), Jayce Boyd (Mets), Chris Garcia (Braves)