Corny dialogue aside the personalities are the same. Megaman didn't exactly beg Roll to come along on his adventure in the OVA. And the sexist thing was only in the first episode, probably added to teach kids a "valuble lesson". While the dialogue was terrible, the character seems unchanged.
I don't think I can agree so much that the OVAs held on to the classic feel of MM over the RS show. The intros are what I'd expect, and some of the end as well as isolated scenes, but the entire middle part dealt with Megaman in the "real world" of Japan for all three OVAs. Moreover, the Robot Masters didn't even recieve any lines of dialogue. Their appearances were extremely limited, which is disappointing since the Robot Masters are a HUGE part of Megaman. The main cast might have been given a degree of "justice", but they hardly appear either (the first one doesn't even have Roll). The OVAs are very focused on MM's time in Japan and that eclipses the MM aspect of the show. And, from what we see of MM's actual world, they're literally just waiting around for the game to start. Which isn't quite what I think MM's world is "actually like" in the games.
I can't even say the OVAs got Protoman right. Sure he's not a villain in them, but you don't get any sence of the relationship between him, MM, and Dr. Light. Here's just there. He's not done wrong, but ... he's not really done right either.
I'm not a fan of RS, but I can't help but think the OVAs were a wasted opportunity. If you want to see anything of how MM's world might be like in an anime the OVAs don't give you any answers. And that's the most disappointing aspect of it, really. I can't say if I'd liked to have seen more by the OVA's creators because what we really got was very, very little in terms of actual MM content. I liked what I saw when I saw it, but I can't say I hated every single second of RS and, poud for pound, RS delivered more Megaman than the OVAs. I guess, just by the math, I liked RS more, but I feel both failed in several key components.