There's something wrong here. The only ways that the HD 650 has less bass than the HD 598 are that you have a defective HD 650 or (and this is much more likely) that you aren't giving the HD 650 sufficient power to drive them properly. There is almost certainly something(s) in your system, staring with your music file to the last piece of equipment to the cans, that is problematic.
I will also add that very few people have found the HD 598 to be fatiquing.
Your description of the D5000 is reasonable, although I don't happen to share it; at least not in degree.
I don't share your taste in music, but for $700 (in the U.S.) I would recommend almost everyone to get the HE 500--and make sure you can drive it properly.
I originally thought this as well... but as a D100 owner there is only one possibility I could think of...
The D100 has been described as very analytical and the amp section as a little polite (but linear) with the bass. I have noticed my own high impedance cans to be a little bit lighter on the bass with the D100 than other amps (although not a lot...) It really was the main reason for me ordering a high end dedicated amplifier to pair with the D100's excellent balanced capable DAC.
So that could explain why the HD650 feels a little bass-light, yes? Of course, it fails to explain why it seems bass-light in comparison to the HD598. However, if he is using the HD598 out of the low impedance output (logically) there could be an impedance mismatch issue (low Z output is built in series with a 40 some ohm resistor) and distortion is often heard as accentuated bass. This mismatch could also explain why he might find the headphone fatiguing... maybe the mismatch is causing some sort of upper midrange or high frequency peak/distortion.
In all honesty, I wouldn't think the potential for the impedance mismatch with the HD598 combined with the reference for the HD650 out of the high impedance output (cleaner, and potentially audibly more bass light) could cause that drastic of a difference, but you never know. This can be easily investigated by trying the HD598 out of the high impedance output (careful) and checking the sonic results... and maybe try both phones out of both outputs.
If you notice the sound improves with the HD598, or even that the bass decreases and the sound becomes less fatiguing... I'd say the money would be better spent on a nice amp to match with the D100 (heard good things about the matching A100 which is well under budget and leaves room for cans as well, or the A18 which is a little above the 700 mark). If you still feel the same way about the HD598 and HD 650 and hear no sonic differences between the outputs, then I'd recommend new headphones all together.
I personally don't think those headphones are the best for rap music... but let's make sure it isn't the D100's amp section that's bugging you, because then getting a new can won't solve your problem
Also make sure the sound file itself is in good shape. Rap music has a bad reputation for being not only recorded poorly, but often compressed and encoded poorly. If the files were downloaded I'd check on those