I think there are key differences in how Eliot and Hardison over-invest in their roles, which is why Eliot fusses at Hardison about it without equating it to what he does himself. (Note: I’m focusing on original series only here.)
Eliot gets over-absorbed because he gets really into what his character does (chef, baseball player, etc.) and loses focus on what the con is trying to accomplish, which isn’t helpful but tends to add authenticity to his individual role. Eliot’s main risk is getting so immersed that he forgets it’s just a con and tries to be that persona rather than doing just enough to fool the mark. He may have some broad-strokes backstory in his head in case someone asks, but his main way to sell his character is just to play the role to the hilt in the current moment. (Prior to the team, he didn’t have a hacker or do long cons, so his main grifting option was to keep things simple, play the role, improv as needed, and hope no one asked too many questions before he finished the job. And be prepared to punch his way out if they did.)
Hardison doesn’t forget he’s playing a role. The part he overdoes is building an “interesting” (often meaning complicated) role and tending to over-act, which tends reduce the authenticity of his performance. The obvious example is “The Ice Man Job,” but it’s the same thing with the overall con in “The Gold Job”–he’s thought out every backstory detail and how to deliver it to the mark, but he lays on the perfectly constructed backstory too hard without reading when to dial back the complexity or exposition. (Prior to the team, it’s implied that he did most of his criminal activity on-line rather than in-person, so the exhaustive planning and documentation was his practical grifting approach.)
If you assign Eliot to be a chef, he’s gonna be a chef. He’ll get distracted from the con by the fact that they’re running out of onions and he just can’t get the flavor of this sauce quite right, but everyone around him will believe he’s a chef. If you ask him where he went to culinary school, he’ll glare at you and maybe throw out some sparse details (trusting Hardison to back it up if anyone tries to check it)–dig too far, and he’s probably gonna be relying on dodging questions or having Hardison in his ear feeding him backstory details.
If you assign Hardison to be a chef, he’s going to have thought out and documented every detail of his backstory, researched his character’s favorite recipes so he can discuss them in detail, etc. You ask him something–anything–about his character and he’ll answer in such detail that your head will spin. But if you tell him the kitchen’s down to its last onion and ask what he wants you to do about that, he’ll be caught completely by surprise and flummoxed about what to do (unless Eliot is in his ear telling him who to send on a supply run to and what menu items to scratch in the meantime).