In my mind EU: Rome had the perfect setup and balance between character vs realm management. In EU3/EU4 I find myself missing the character aspect, there just isn't as much happening as there is in CK2. In CK2 I find myself missing the ideas and the larger picture stuff (I'm also not too fond of titles, endless vassal wars and levy micromanagement). In EU: Rome a new dynasty/barbarian tribe/consul could come to power in your realm and you would assume control of him, which to me is the single best feature of EU:R. This gives you an incentive to try and keep good rulers on the throne while also allowing for barbarian invasions/coups etc to happen.
EU: Rome also had some brilliant features like general loyalty, governor corruption, interesting civil wars and ideas (which CK lacks, a big mistake in my mind). To be honest I think the EU3/4 franchise would improve a lot by adopting a few of EU:R's ideas. By having a couple (10-15) characters for big nations like Castille and France which act as your generals/court advisors/royal family members/crown agents (spies/conquistadors etc) and have them gain traits (improvements to tax eff., trade power etc, missonary chance etc) would increase playable content by a lot (think CK2 light, no marriges, no titles).