In the Web Comic Genos is largely The Worf. An ostensibly powerful combatant, who ends up becoming little more than a measuring stick for how much stronger the new villain (or non-villain) is. Meaning he gets handily beat up on a regular basis, and doesn't need to serve any other purpose than giving a brutal display of how strong his opponent is. Genos in particular tends to serve in that limited basis, doing little more than providing exposition in addition to getting his butt whupped.
What victories he does have are generally off-screen. You may recall the Machine God that Genos fought while Saitama tracked down King and learned the truth of King's power. In the Manga this is a highly detailed fight where we see exactly how Genos handles the fight and how tough it is. In the webcomic the fight occurs completely off-screen. The manga has, subsequently, significantly increased the apparent power of Genos, simply through giving us more exposure to his actual successes (or even draws).
As Orochi is a Manga original character, so too is the Psykos-Orochi fusion. We've been told by Murata that Orochi was meant to give Tatsumaki more of a challenge than any one fighter did in the Webcomic. However, Tatsumaki does still have certain issues in the fights that ensue after she lifts up the entire Monster Association base in the webcomic, and Genos does intervene to help her out in that fight as well. This occurs in Chapter 71 of the webcomic. The end result is that, while he effectively deflects an attack from a Dragon-level threat to bail Tatsumaki out of a bad situation—much as with the manga scene you reference—he does no real damage to anyone and immediately loses his arms to a counterattack. While he doesn't exit the fight immediately, attempting to continue with nothing but kicking power, he is effectively a non-factor doing little more than providing minor distractions and expository observations from that point on.
As a general rule, Genos does go through an upgrade cycle after every failure, both in the webcomic and manga. This occurs when he gets repaired. The manga has entire arcs that do not appear in the webcomic, though, such as the tournament, as well as significant alterations to various fights. I believe there are two upgrade cycles that are subsequently unique to the manga, due to their preceding fights not existing in the webcomic:
- Goketsu. This character and the tournament arc do not exist in the webcomic. As such the bodily destruction and subsequent repair+upgrade exists only in the manga.
- Elder Centipede. In the webcomic, Elder Centipede is not only not fought by Genos, but is not even fought and defeated by Saitama. In the webcomic, he's bested by Garou, who takes up the fight after Metal Bat.
If we take Genos at his own word about his powers, then immediately preceding the Manga scene you reference he says that he is now able to destroy meteors; presumably his baseline is the meteor he failed to deal with earlier in the story, that was ultimately taken out by Saitama. That meteor was assigned the threat level of Dragon. In the Web Comic, however, Genos does not make any claims about being able to defeat a Dragon level threat (meteor or otherwise) until after his repair+upgrade cycle following the Monster Association arc (and even then the claim seemed somewhat questionable, as he almost immediately loses an arm to a Demon level threat, but later on he does seem to perform well in comparison to Flashy Flash).
So the net conclusion is: he's been upgraded more times in the manga, but for trivial reasons (more necessary repairs were added); but he seems to have been upgraded to "one level" higher, being able to deal with a dragon-level threat pre-MA fights rather than post-MA fights.