It is even worse when I try to GM DnD. As a GM, you have to wear down the party with multiple encounters of attrition before you can begin to challenge them, especially at the higher levels (here I agree with PaStaav too). It becomes a game of 'DM may I short rest here?', and that's a drag.
Ah, no, you don't need that to challenge your players. But you need to take into account the pace of encounters. The default D&D hypotheses are 1) characters spend most of their resources between two long rests, and 2) characters do not try to avoid encounters. And the idea was to have attrition because it is much more comfortable for players to manage their resources if they have perspective (and thus can take a long test :p).
Now remove the idea of attrition most of the time (just not *all* of the time). Have each encounter require most of their resources, or at least, most of their critical resources. And give them time to prepare if they are careful and inventive, and if they use their *other* resources (those that are not needed in combat, and that include money, contacts, and brains) appropriately. A good D&D encounter is one where you feel you manage your resources *during* the encounter and have to determine your main goal carefully and circumvent most of the unnecessary attrition, because attrition will play against you. It's even better if the players can force their opponents to spend resources while they themselves do not.
The best D&D campaigns are those where you don't fight often, but where you have to manage your resources each time you do. That's why I find it better than RM for heroic high-fantasy: in RM, any resource management can be voided by the whims of a single die roll. In D&D, less so. Players can see the tides turning for or against them. In RM, it is possible as well, but it is also possible to be felled by a single blow from a lesser opponent. Some people do like that, others do not (I count myself in the third category: those who think that combat should not be a challenge all by itself, but should only be a side show - combats are not meant to be really challenging, but I want the characters to understand why they willingly enter a fight and what they expect to get out of it).
Now I also happen to think that D&D is not good for character customisation. It relies far too much on stereotypes, and uses myriad of more or less balanced subclasses to provide variability, and D&D4 and 5 were actually a step backwards compared to D&D3 in that regard. RM is better only by virtue of going halfway between pure class-based and pure skill-based, but then gets mired down in the same illusion of detail as other games (everyone thinks their particular situation is a special case that would be best resolved by having a separate skill). There is no hard look at what the game really is about, what is considered essential (and, as such, requires differentiation) and what is merely character fluff.
One thing I got from BESM and I thought was a very good idea was that skill price varied not according to 'classes', but according to genre: the skills that were most central to the genre you wanted to play were the most expensive ones. Peripheral skills cost less to develop. This is the kind of game design thinking I would have liked RM to take for a 21st century reboot (along with having all rules condensed into 100 pages or less, tables included, because let's face it, rules do not need to take more than that): have the game designers think clearly about the kind of games RM was about, optimise the rules for that kind of games, trim all the fat from previous editions, standardise the core mechanisms, and be very explicit about it.
