Question about IEM choice

Last week I broke my pair of in ear headphones, and now I've decided it's time to upgrade to something nicer.  I prefer a flatter, more neutral sound, so after a bit of research I ended up always coming back to the RE-400.  After watching the recent video about the HM-700 (which includes these headphones) I was left wondering if it would be necessary for me to get the player as well.  What kind of sound quality difference would I notice coming from my phone (nexus 5 using neutron with the highest audio playing settings) as opposed to the player?  Also, are there any other IEM I should consider?  I prefer and need the neutral or flat EQ, simply a matter of taste and use (these will be used for some basic audio production for a few weeks/months).

TL:DR- For under $100, any other "flat" headphones to consider other than RE-400?

Is the HM-700 that big of a jump in audio quality over a phone with a high quality player?