There is a lot of non sense people sprout when it comes to DACs.
The fact is:
1. Either a dac is transparent like apple products, benchmark products, Odac etc
2. Or it isn't like audio gd which is colored or lots of other such companies
Between transparent DACs the differences are fairly small. Going from an iphone inbuilt dac to a $2000 benchmark is going to have the same sound, just slightly smoother and less harsh. There will be no other difference. It is definitely worth the price if you have money to spend in huge amounts, otherwise no!
The placebo people get is because different DACs have a line output at different volumes. Once you match the line output to within 0.1 db of each other and provided no component is running out of steam and provided you do a double blind test, the difference between all DACs starting from the iphone dac to $5000+ DACs will be 1-5% of each other.
The only difference you get with a better dac is a slightly smoother and slightly resolving sound and very slightly at that.
And good speakers/headphones ideally sound decent out of anything and get better with better gear. Gear which is finicky is just not designed as well as other stuff and is revealing for all the wrong reasons. Like hd 650 scales very well but sounds better than most stuff nevertheless. Of course in its price range and lower that is.
Honestly, under $200 you aren't going to get much of an improvement over the iphone or iPod dac. There are lots of sub $500-1000 CD players which perform worse than it. And nobody has preferred them unconditionally in a double blind test either. And the differences are really small anyway.
The best you can get under $200 is either the asus stx or Odac. The iphone dac is slightly behind the two. To really get anything even slightly better you need to go up to the schiit bifrost or asus stu/one.
What is your rig?
Unless you have a hd 650 or higher gear you don't need to spend too much on a dac. With hd 650 and over $200 for a dac isn't ideal anyway, just a temporary measure.