I've compared the two directly. The biggest difference between the two are soundstage. As a closed headphone, the M50 feels almost congested in comparison. I highly recommend buying an open headphone over a closed one. Even a semi-open one (like the Denon series) are fine. As another poster mentioned, another difference is that the M50 is bassier. But I found the bass to be somewhat loose and leaking into the midrange. Same with the HD 558 actually, though it's not nearly as bassy as the M50. M50's bass was a little too much for me, since I listen to classical and acoustics music. And its recessed midrange was a turnoff.
I know the M50 is a popular recommendation but there are other closed headphone options as well (Shure 840, Sony series, V-Moda line, etc.). It's a great headphone for 100 dollars but now they go for 150 dollars. Not sure if they still leave up to the hype
at that price.
In addition, I found the HD 598 to be VERY versatile. Do you perhaps game online or watch movies? The HD 598 excels in both categories due to their phenomenal soundstage. Depending on what headphones/ earbuds you are using right now, the HD 598 might seem bass shy at first. I also had that experience. But remember you could ALWAYS EQ the sound to increase bass quantity AND your brain will naturally adapt to the bass of the HD 598 over time, which a lot of people actually find to be bass neutral, not bass lean. The bass is pretty punchy (that's a good thing) and extends better than the HD 558.
I would go with the HD 598 but it really depends. The neutrality of its bass is what makes it so versatile in multiple genres. It's not the best for Metal, Dubstep, etc. because it could use a little more "speed" and "bass" that closed headphones offer. But it's not exactly bad with those genres either. The M50 on the other hand is not very pleasant with classical/ acoustics music imo. Have you ever looked into the Denon D2000? They are like a superior M50 (imo).
It seems like you should do a little more research on headphones. Here are some starters: Denon D2000, AKG Q701 (amp required), Beyerdynamics DT 880, Shure SH840, Grado SR 80.