best? it really depends on what you're looking for as a sound signature. all have areas they excel at and areas they do not.
there are 4 classifications i'd put headphones into for signatures (or bass levels as well). to try and give you an idea how much bass the cans will be able to provide i'll describe it again.
bass light: can give punchy bass but without real depth. not bass-less but bassheads may feel that way. good for gaming. things like the ad500x fall into this category.
neutral: can give punchy bass with a little more depth. while not capable of deep low level bass they do not give the feel of being super light on bass either. bassheads may not be happy but most normal people may be. while not quite as advantageous for fps gaming as bass light cans, they do have a little more oomph to them so are a bit more fun. neutral still can sound a bit more flat compared to v-shaped cans, but they hold the midrange between bass light and bassy. things like the hd518/558/598 would fall into this category.
bassy: capable of more than average bass. many are capable of deep low tones while not affecting clarity of mids and highs. certainly some low end punch which makes bassy songs fun to listen to. bass covers up footsteps in games so they arent as advantageous as ligher ass headphones for gaming but its more than possible to game competitively with them if you prefer bassy signatures. the advantage of bass light headphones is not going to trump skill. things like the m50, 770/880/990 fall into this category
bass cannons: capable of the most bass you fill find on headphones. bass tends to be extremely powerful with much quantity. often sounds a bit bloated and in some headphones tight while others flabby. headphones in this category focus on bass alone so treble/mid quality suffers and can sound muddy. things like the sony xb would fall in this category. i would not suggest these for gaming or any use unless you are an extreme basshead and its the only way to satisfy you.
for you, i would say anything from the neutral or bassy category would suit you. its hard to give you an estimate of bass but this is generally the case for most people who arent bassheads.
the hd598 is not weak with bass but not strong either. its not like there is going to be none at all (even bass light headphones are not completely without bass). its neutral.. bass is about the same level as the rest.
example of dt990 vs hd598
http/graphs.headphone.com/graphCompare.php?graphType=0&graphID%5B%5D=2851&graphID%5B%5D=2141&scale=30
example of hd558 (which is almost the same as hd598) vs ad700 (old version of the ad700x)
http/graphs.headphone.com/graphCompare.php?graphType=0&graphID%5B%5D=533&graphID%5B%5D=2661&graphID%5B%5D=2861
880 990 770
http/graphs.headphone.com/graphCompare.php?graphType=0&graphID%5B%5D=2751&graphID%5B%5D=2241&graphID%5B%5D=2131
chart site is down or i'd link them all in one. heres an idea of what the frequencies are like in terms of audio
https/static.gearslutz.com/board/imgext.php?u=http%3A%2F%2Fi113.photobucket.com%2Falbums%2Fn204%2Fsaneoner%2FScreen_Shot_2013-06-25_at_4_zps62xhdqof.jpg&h=92d6236498075c1bafb4e410cd9398cb
the iphone (like all apple products so far) have decent amplifiers in them (perhaps this may change with them wanting to put different jacks on their phones...) so often sound better than cheap onboard audio. given that you mentioned this, i'd definitely suggest upgrading your onboard audio when using better headphones. for easy to drive headphones this could be simply something like a soundcard (for hd598) or for harder to power cans, i'd suggest an amplifier and dac or amplifier and cheap soundcard. (beyerdynamics cans)
so.. thats alot to read.
tldr, anything from the neutral to bassy category would suit you. hd598, dt880, dt990, dt880 would all work. hd598 would be cheaper to amplify (soundcard) while beyers would be more expensive. personally given that i have a m50 and like the v-shaped signature (its fun sounding) my own upgrade preference would be to the beyer 770 or 990 but to each their own. the beyers will have more energy and be more articulate sounding than the 598 (but at the same time, this may be fatiguing for some.. it depends on if you like detail or not)