I've gone over my general starting pitcher considerations here.
Selection Sandy Koufax
When it comes to "best ever" discussions, there are often two competing philosophies: what was a player's peak versus how long was the player good. Dominance versus duration, if you will. Of the players on my roster, Koufax is the one most firmly in the dominance camp. He only pitched for 12 seasons and the first few were more promising than great.
For the first six years, Koufax pitched like Nolan Ryan's left handed kid brother. Lots of strikeouts, sure, but lots of walks, too. Then, around 1961, Koufax figured it out. His walk rate dropped from 13.3% in '60 to 9.0% in '61. And it kept dropping, hitting 4.8% in '63. And then it stayed low. Still a lethal strike out pitcher, by 1962 Koufax was the best pitcher in baseball since Walter Johnson. And so he remained until 1966, when arthritis forced his retiredment at age 30. For six years, from 1961 to 1966, Koufax not just great, but legendary.
Koufax's legend and career line, 2.76/2.69/75/75 (ERA/FIP/ERA-/FIP-) benefit from his retiring at his peak. After all, Steve Carlton had as many great seasons and a much longer career. However, even had he not been arthritic and pitched another five to ten years, even had he lost some of his stuff, I doubt Koufax would've lost the incredible control he had learned. And he would have had more years of both power and control to balance the effect of his early wildness on his career line. His career 2.93 K/BB isn't the Koufax we remember. 5.38 K/BB, put up in his penultimate, 1965 season... that's the utterly dominant mix of power and control that Sandy Koufax deservedly conjures. That season is as characteristic of his amazing '62-'66 run as any other: 2.04/1.93/63/63. It was his strikeout peak, with a 29.5% K rate.
So it is Koufax over Carlton. Lefty was great for a long time, but some time around 1961, Sandy Koufax transcended the art of pitching.
Another legendary lefthander, Carlton was a very good to great pitcher, but mostly in the duration over dominance category until later in his career. Starting in 1977 (or maybe 1980, depending on how much you wish to credit good fortune and defense) to 1983, Carlton enjoyed a stretch of dominance just shy of Koufax's lofty peak.
I say mostly because Carton's 1972 season is one of the greatest of all time. 1.97/2.01/55/60 with with 346.1 innings pitched. (That's the kind of season that destroys pitchers, look at Bob Feller's 1946.) It's the second lowest FIP- of any season since 1920 (the live ball era) with over 300 innings (Bert Blyleven pitched just over 320 in 1973 and was one point of FIP- lower). It's also the 7th lowest in ERA-. 346.1 innings of dominance. It's worth noting that were bad that year, average fielding and poor hitting (a team wRC+ of 80) with a team record of 59-97.
Carlton's career line, across 24 seasons, is brought down a bit by his post Phillies struggles from 1986 to 1988, but is still a strong 3.22/3.15/87/86.
You might call Doc Gooden the mirror image of Sandy Koufax. Not only is Gooden right handed where Koufax was a lefty, Gooden's career looks like an inversion of Koufax's. For the first 5 years, Gooden was brilliant, particularly his first two. Then, perhaps because he was overpitched, perhaps because he lived too hard a life style of the field, Gooden fell to earth. By 1993, Gooden was struggling to be a league average starter*, though he hung on even as his control left him (and managed to stay effective until 2000) in another mirror to Koufax's career. Even with his struggles, Gooden's career line is strong 3.51/3.33/90/84
Gooden started his career as best pitcher in baseball. His 1984 rookie season has to be the best by a pitcher, ever: 2.60/1.69/74/49 with a 31.4% K rate and 218 innings pitched.
*For what it's worth, an average major league starting pitcher -- or any player -- is already a great player. At the major league level, the talent distribution isn't symmetric, it's greatly skewed. Roughly 70-75% of major leaguers are below average.