Jason Heyward is a better baseball player than Gerardo Parra. I just want to start by getting that out of the way.
I won't belabor the arguments that Jason Heyward is very good at baseball. He is. There is a reason that if the Cardinals sign Heyward to an extension before next season, it will be far and away the largest contract to which the club has ever signed a player.
Not only is Jason Heyward a great player, but he is also a young player. As has been mentioned repeatedly on this website and many others, players a few months past their 26th birthday, which Heyward is, simply don't come up for free agency very often. And even fans who are normally hesitant to spend big money (even if it's somebody else's money) are able to convince themselves that Jason Heyward is the guy in whom you want to invest, because even if a team signs Jason Heyward to a ten-year contract, he comes off the books at 36. A team may overpay somewhat in the 10th year, but it would still be perfectly reasonable to expect a viable MLB outfielder.
With that said, if the Cardinals are going to invest long-term in a player, there must be a certain level of confidence that the investment will work. In the cases of the other three major corner outfield free agents, Justin Upton, Yoenis Cespedes, and Alex Gordon, there are serious questions about long-term viability. Upton, though only 28, has never been a great defensive outfielder and, even if his hitting continues unabated, may be a liability in the field in the coming years. Cespedes, who turned 30 in October, had easily his best MLB season in 2015, but has otherwise been a good-not-otherworldly player, and there is a risk of paying for his inimitable 4th season rather than paying for the solid player that his first three seasons suggested he is. And Gordon, 31, is similar to Heyward in that he has a good bat but a great glove, but at 31, he is just entering a period in which defensive decline is presumed and where further offensive growth would be shocking.
Gerardo Parra, however, is in a different class of free agent than the aforementioned outfielders. While Heyward, Upton, and Cespedes are all likely to command contracts of no fewer than five years, Parra's expected contract is a far cry from those totals--for instance, MLB Trade Rumors initially predicted that Parra, 28, would sign a three-year deal worth $27 million. And as much as I would love another decade or so of Jason Heyward patrolling right field at Busch Stadium, there is eventually a breaking point with regard to contract size. I don't know if that point will be reached, and where that point is varies greatly among Cardinals fans, but if the Heyward market does get completely out of hand, there is clear upside to Gerardo Parra.
For those unfamiliar with Gerardo Parra, he had his best season in 2013, when as the right fielder for the Arizona Diamondbacks, Parra was worth 4.5 Fangraphs WAR and 6.1 Baseball Reference WAR. He was essentially an average hitter, sporting a 99 OPS+, but he was second only to Manny Machado in MLB in Ultimate Zone Rating. Parra has started 344 career games in left field, 149 in center, and 319 in right field; however, recent years have skewed towards playing in right, with LF-CF-RF starts since 2013 numbering 65-67-267. He won a Gold Glove in left field in 2011 and in right field in 2013. Parra has a career 97 OPS+, which suggests that he has been an ever-so-slightly below average hitter.
The overall story of his career is that he's basically a Walgreens brand Jason Heyward, and as such, he may be a last resort present for procrastinating shoppers as Christmas approaches, though he will probably at least exceed the joy that comes from a Chia Pet. In 2015, Gerardo Parra actually had an uncharacteristically poor defensive showing, yielding below-average UZR in all three outfield spots. But these are outliers for Parra's career--it was his first below-average defensive season in right field ever, and his first in left field since his rookie season of 2009.
Defensive metrics tend to require larger sample sizes before drawing anything resembling educated conclusions than batting stats, and while Parra's defensive dip in 2015 isn't nothing, I'm more inclined to trust one year's worth of data at the plate than in the field. And in 2015, Gerardo Parra, following three consecutive (slightly) below-average seasons by OPS+, posted an OPS+ of 110. Parra actually had a 139 OPS+ with the Milwaukee Brewers--to put that into perspective, the aforementioned Yoenis Cespedes posted a full-season OPS+ of 137. But after a trade deadline deal sent him to the Baltimore Orioles, Parra floundered to a 69 OPS+ in the American League.
Now, I can't even pretend that I believe Gerardo Parra magically figured out the National League and that a 139 OPS+ is what he is now. But the 110 OPS+, accounting for his 2015 peaks and valleys, did not come by accident. He hit a career-high 14 home runs (one more than Jason Heyward, for whatever that's worth) and although his BABIP was a tad higher than his career levels, this was not purely a matter of luck--his line-drive percentage was up and his ground-ball percentage was down. This might be what he is now. And even if it isn't, the 69 OPS+ almost certainly isn't either, and in the worse realistic scenario, Gerardo Parra will be a slightly below average hitter for the next few years, though far from a catastrophe.
Additionally, his career lefty/righty splits suggest that Parra can at least excel in a platoon. While the idea of paying a player what Parra would likely cost to participate in a platoon may sound like a preemptive concession of defeat, as the lefty bat, Parra would still get the solid majority of plate appearances. And in his career, Gerardo Parra has a solid .767 OPS against right-handed pitching. With the collection of right-handed outfielders currently on the Cardinals--Matt Holliday, Randal Grichuk, Tommy Pham, Stephen Piscotty--the club could afford to sit Parra against lefties, even if Piscotty platoons at first base with Matt Adams or Brandon Moss (which he should), and save Parra for late-game pinch-hitting or defensive replacement duty.
The obvious appeal to signing Gerardo Parra as opposed to signing one of the high-end outfield free agents, including Jason Heyward, is that he's probably looking at a three or four year contract. If Parra's career suddenly craters, his contract is less of an albatross than a seven-to-ten year deal. But the timing also works perfectly because, if Gerardo Parra signs a three-year deal, the Cardinals can position themselves for a big-name signing in the Free Agent Class of 2018. Here's a quick glimpse at the Class of 2018, as listed by Tim Dierkes of MLB Trade Rumors.
Potential free agents after '18: Harper, Kershaw, Jose Fernandez, Donaldson, Harvey, Keuchel, Machado, Pollock, Price, McCutchen, Brantley— timdierkes (@timdierkes) December 8, 2015
That's eleven names. Eleven! A.J. Pollock and Michael Brantley are among the least exciting names in that group, and each was worth 9.9 fWAR over the last two seasons. The free agents will be there whether the Cardinals sign Jason Heyward or not, but it would certainly be easier to find room in the budget for one or more of these guys without extending Heyward.
I would still prefer to sign Heyward, because it's impossible to know how attainable any of these guys will be in three years (almost certainly, some will sign extensions with their current clubs before they ever reach free agency). But in case Jason Heyward does get away, signing an underrated and efficient bridge to a rich free agent class who can fulfill many of the same roles of Heyward in the short term may be the next best thing.