Yeah I can attest to Rdms pulling a truckload of hate on my War while leveling, especially compared to other DPS I was playing with (Drg/Sam/Mch: all at the same high skill level). A lot of War's hate "issue" seems to stem from the fact that it doesn't feel like Butcher's Block is worth using that often once you have decent hate established. Storm's Path heals you and doubles the amount of beast gauge you get (and throwing out more inner beasts will make up the potency difference, it feels like), so I found myself really only using a BB combo once at the start of some fights, and for group packs, not really at all. Steel Cyclone and a random Overpower here and there consisted of the majority of my hate-grabbing actions.
I'm not a number cruncher so I haven't factored in how much of a DPS gain/loss it is swapping out more BB's for Path to keep the beast gauge flowing, but considering our 66 passive knocking off infuriate CDs whenever you eat your beast gauge on a big move, I'm playing a mental game to try and stack up as much as I can, which means I'm not focusing on staying horribly out in front of my DPS in actual hate.
Rdms just have a habit of creeping up so on me so much faster than other classes. I haven't tested playing with Brds or Blms yet.
In terms of Wars somehow having shit hate generation? No one should be saying that. If a War wants to keep hate, they can keep hate, but at what cost? We're so used to pushing for a balance between rock-solid hate and as much damage or mitigation as we can get. Its going to take me some time to figure out a sweet spot, and its going to depend on how well-geared I am vs. the mobs I'm fighting.