From my experience, the biggest difference I could hear without effort is from going from one headphone to another, with DAC's, it's a more subtle change. Mind you, I'm NOT against the idea of getting new DAC's and such, but the benefits from going from rather 'meh' can to a better one (like the DT880/DT990) is more noticeable when compared to going from onboard (as long as it's decent enough) to external DAC's (as long as onboard supports the audio formats you use and gets loud enough, for me, all my DAC combos and stack have to support DSD format since I have more than 4TB of DSD 64/128 goodness). Seriously, I have more than a dozen cans, going from my Oppo HA-1 to my Gustard H10/X12 stack, I do hear subtle differences between them, but going from my ATH-AD700X to my DT990 600 Ohms was literally night and day difference.
IMO, get the DT990/DT880 first, but only if you know you like the sound signature, and if onboard doesn't get loud enough (shouldn't be a problem even if you get a 250 ohm version), then look for an external amp (or DAC combo/stack). Of course, my point is moot IF OP has budget for BOTH headphones and DAC upgrades simultaneously. If so, then hell yeah, go for broke!
Oh yeah, don't simply look at impedence (Ohms) and say this or that is harder to drive, you must also note the sensitivity, the higher the number, the easier it is to drive. Look at the HE-6 for example, it's rated at only 50 Ohms, yet is acknowledged as one of the hardest to drive ortho cans around, this is due to its efficiency (not the same as sensitivity, but should give you an idea) rated at a measly 83.5dB which is why it requires so much raw power to drive it. I've even read of some using speaker taps (with adapters) to drive their HE-6. My Beyerdynamic DT770 250 Ohms is rated at 96dB, yet I'd bet all I have that it's easier to drive compared to the HE-6.
Edit - Please wait for some audio savvy guys to reply, I'll admit that I'm rather new at this as well....
Oh yeah, with regard to comfort for both open or closed back cans, both can be quite comfortable (difference could be clamping force) but, like you, I'd remove my closed back cans after an hour or so, this is due to my ears getting quite warm and/or sweat. I find I don't sweat much with open back cans but YMMV. As for clamping force, again this varies from person to person, I don't mind a higher clamping force, my DT770 Pro definitely has a greater clamping force compared to the DT990 Premium, but I don't mind....maybe because I'm one tough hombre.