I went from training exclusively with the gi for a few years to training almost exclusively without it, and I can tell you both from my own personal experience and from witnessing many others make the same transition that that is not the case. Either way there's going to be a steep learning curve.
A purely no-gi grappler trying to adjust to the gi game will face a number of problems. While his repertoire of techniques will be intact (since every no-gi technique is theoretically possible with the gi), some of them will be less effective than usual as there will be gi techniques that can counter them. Most of those problems will be when he is in his opponent's guard; maintaining posture, defending armbar/choke/sweep attempts, and passing the guard are all more difficult when the guy on his back can use gi grips. Then there is the whole issue of collar chokes - something he has absolutely no prior exposure to, and therefore will have a tough time defending.
Despite all those difficulties, however, the no-gi grappler does have a number of advantages that will make his transition to the gi easier. While he will have to add a lot to his game, there really isn't much he will have to subtract from it. His offensive game, both from the top and from the guard, will be solid because the absence of gi grips will have forced him to develop tight body control. For the same reason, he will have developed excellent hip movement to aid pass defense and sweeps. And while he will bring a relatively smaller number of techniques to the table, he will be very well versed with those techniques. Basically, he will have a solid foundation on which to build his gi game.
The purely gi grappler moving to no-gi faces the opposite challenge - a lot of what he knows doesn't work anymore. All collar chokes and a large number of sweeps are immediately thrown out the window as there is simply no way to perform them without the gi. Many other techniques are either flat out ineffective or require extensive modification to perform without clothing to grab onto. Anything that requires controlling your opponent's body - setting up guard passes, breaking down the opponent in your guard, maintaining position, sweeps, submissions - will be more difficult without the gi.
The biggest problem with guys who previously trained entirely in the gi (myself included) is that many of them have developed bad habits by allowing grips to substitute for proper body control/movement. When you have a sleeve to grab onto, you can get away with being a little loose with your legs in an armbar, or a little lax with your hip movement in a sweep. That's not the case in no-gi. As a result, they find themselves having a hard time finishing submission attempts and just controlling their opponent in general, even against people with far less overall grappling experience. Unfortunately, rather than fault themselves for using poor technique, many choose to blame it on strength/speed/slipperiness and talk about how much more technical the gi game supposedly is.
Basically, both gi and no-gi grappling present different challenges and force you to develop different aspects of your game to a higher level. Neither is better or more complete than the other; in fact, a complete grappler would train in both. Gi players would get a lot of benefit from working more without it, as the body control they develop will make them that much more effective when they add the grips back in. No-gi players would also benefit from working more with the gi, since the larger number of sweeps they face will force them to improve their base quicker. Either one stepping into the other's world for the first time is going to find certain areas of his game severely lacking, but if he takes that opportunity to improve himself rather than whine about how his style is so much better, he'll gain by doing so.
