Today's game can be just as much roll-playing, it highly depends on the group. One of the things that drove me back to B/X and ADD was the sheer number of min-max players and rise(!) of murder hobos in 5e vs. even 3e/3.5/pf1

Most of the early old-school stuff was way too deadly for players to be murder hobos or try to solve everything with combat - if you went into Caverns of Thracia at level 2 as a murder hobo you're just going to die over and over and over again. It'll be endless TPKs. Right now I'm two years into DM'ing an Arden Vuul campaign, running a mix of OSE (Streamlined B/X) and OSRIC (ADD 1e) rules, and it's really only the past 6 months or so that my players have felt comfortable engaging in regular combat - before then they might have spent a whole session or two trying to stack up every advantage they could because they never wanted to be in a fair fight.

And from my experience with a whole lot of OSR play over the past 6-7 years is that this is the sort of feel most OSR players are after. They're not wanting to play late ADD 2e, Dragonlance era, where the shift to the more heroic play started happening - they want to have to think and outsmart things. Faction interaction was also huge in the more sandbox environments, and that was where most of the roleplaying occurred then, and occurs now in the games I run. The players RP a bit with each other, but not as much.

Modern D&D is a kitchen sink approach that tries to solve every possible playstyle, and that makes it popular and reasonably good at most anything people want to do with it. But I don't know that there's any facet of it that it does as well as other systems.