It's not a real issue but just a negative point, the H4N hiss with some mics
Here listen to the H4n with a Condenser Short Shotgun Mic & the Dynamic Omni Mic sound and you hear what i mean.
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Tascam DR-40 does a better job bit with some but a worse job with others.
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I use the rode ntg-2 and as you can hear that sounds very well on the tascam but with the H4N you hear a hiss with the shotgun and that's often the type of mic most use.
So basically non is generally better, you just need to find out which work better with the mics you want to use and go for that.