The prime nine
While not in complete agreement, there is a good deal of consensus when you look at the leaders in team history, by Fangraphs WAR (fWAR) and Baseball-Reference WAR (bWAR). Indeed, nine players appear on the top ten lists for both metrics, so those are the ones we'll look at in more detail. [In case you're wondering, the exceptions are Jay Bell, 9th by fWAR but 12th by bWAR, and Gerardo Parra, who was 10th by bWAR and 11th by fWAR] Here are the overall stats for the nine players, along with their bWAR and fWAR. The list is sorted by the average of the two metrics.
The two do agree that, in terms of total value, Goldschmidt trails Luis Gonzalez. But look at the huge difference in playing time - Gonzo played 573 more games, the better part of four full seasons, for the Diamondbacks than Goldy has to this point. On the other hand, Gonzalez was already into his thirties before he arrived in Arizona. Though if you want to take that into account, over his age 23-27 seasons (so, the same as Goldschmidt), Gonzalez played a similar 658 games, but put up 13.2 bWAR - while certainly very respectable, it's well short of the current first baseman's numbers over the same part of his career.
A couple of random thoughts on the list above. Forgot how good Steve Finley was, especially considering he didn't play a single game for Arizona before his 34th birthday. Among all major-league center fielders in the integrated era, only Willie Mays put up more bWAR after their age 33 season. He did likely stick around two or three years too long, but was gone from us well before that point. And in case you're wondering, if we had hung on to J-Up through the end of the contract extension negotiated with him, and he had performed as he did elsewhere, he'd be ahead of Goldie, with figures of 24.7 and 26.5 respectively - though, again, in a lot more playing-time (1,184 games).
WAR1, WAR3 and WAR5
To try and figure out the "best" position players, we really need some way of adjusting for playing time. All of our "prime nine", with the exception of A.J. Pollock, played at least five seasons for the Diamondbacks, so why not look at their "best" five seasons, by WAR? Obviously, that will still benefit those with long careers, as they will have had more rolls of the dice - but that's probably as it should. And, at least then, we should be doing a better job of comparing like with like. Here are the best one, three and five seasons for each of the prime nine. For simplicity, I'm sticking to bWAR here.
Goldschmidt is handicapped by the fact that he only just has five season with Arizona, and that includes his rookie campaign, in which he played 48 games. The 0.4 WAR resulting allow Gonzalez to come from behind and pip Paul in WAR5, after trailing in WAR1 and WAR3. Conversely, if you compare Finley and Upton, the latter's "streaky" nature becomes apparent: Upton had easily the higher peak season, but his troughs were also deeper - between his best seasons (4.0 and 6.1 WAR), Upton struggled to a 1.5 WAR year. A.J. is like Paul, with a rookie season of just 31 games, meaning his WAR5 total is actually more like WAR3.2, hence the asterisk beside it.
Once you get past the top three, there is perhaps surprisingly little range in WAR3 and WAR5. Though, damn, would you have said that Counsell's best season was better than any ever put up by Young or Finley? That was 2005, and was mostly the result of Craig's wizardry with the glove. His defensive WAR that season was 3.4, which is the second highest of all-time, at any position, by a Diamondback - someone here will be glad to learn the all-time #1 was Gerardo Parra's 4.0 in 2013. As a yardstick for how good Counsell was for us, Nick Ahmed's 2015 is third omn the list, and was worth 2.8 defensive WAR.
Two things currently make the question anything less than rhetorical. Goldschmidt, obviously, has much of his future in front of him, and it seems almost certain, good health willing, that by the end of 2016 he'll overtake Gonzalez in bWAR and WAR5, with fWAR falling sometime in 2017. At the current point, however, comparing their career numbers against each other, it's still debatable. Right now, you could argue the case for Gonzalez or Goldschmidt as the #1, and I would probably agree completely with you, at least on Tuesday, Thursday and Saturday. Monday, Wednesday and Friday, I'd vehemently disagree. I take Sundays off.
The other trump-card which Gonzo has, and Goldy doesn't yet, is an iconic moment. No, make than an Iconic Moment. And they do not come more iconic than a walk-off hit in the bottom of the ninth, to win Game 7 of the World Series. That guaranteed Luis will never have to buy another drink in the state ever again [I know we have personally offered to buy him dessert at least once!]. and remains the Iconic Moment in the state's entire sporting history - though the Cardinals might have something to say about that in the next month... If Paul can deliver something anywhere near as memorable, the mantle will be well and truly passed, regardless of any statistical measure.