In order to have more colorful drama, corps can take more colorful roles. RG is the most explicitly honorable corp. AXE is the corp most friendly to newcomers. M2S is the most explicitly griefer/untrustworthy corp. However, there are many others (ECORP and HUN, for example) that have bases of support (europe in general and hungary in particular), but no in-game role.
I think you might wish to reevaluate these descriptions a bit. How is RG the most honorable? M2S, while they tout the "bad boy" image, really haven't done anything to merit the title- and their behavior on these forums is actually pretty respectable. On the other hand, are you sure that ECORP and HUN have no roles? They seem to be active within their alliances.
Corps might differentiate themselves by preferentially recruiting from one race (e.g. theodica pilots) or role (e.g. commodity haulers and traders, damaged-goods purchasers/repairers/recyclers, mercenaries). They could differentiate themselves by committing to a location (something like the NORHOOP alliance), or by their policy towards other corps (e.g. NRDS, or always neutral but sells to everyone, or tit-for-tat, or grim trigger).
I agree with this- so far, no corp stands out as unique. They all seem to be following the same lowest-common-denominator route, with no efforts at differentiation other than the puffery in their recruitment fluff.
To get back to your main point: yes, I agree that some differentiation would help- not only in attracting new players, but also in getting rid of the "EVE with bots" description.