I can give you a good comparison of what i've made up for the last moth after a looong searching.
Build Quality
Some will say Redmi 1S, no doubt it had got a good bar shaped design but its plastic akin to Moto E, so no issues with wither of them.
However the simple cut-to-cut design of Redmi appeals me.
Performance
Even while having a QS 400 @ 1.6 Ghz, the Redmi has a lot of issues in UI. I have read review of buyers that they are have UI crashes and lagging, comparing to moto e, moto offers a much better lag free interface with a better RAM management.
Coming to the gaming performance both of them are at par, they can *run* any game presently found at the Play Store. but Redmi's got heating issues. Unlike Moto it heats up a lot to about 45C max while gaming and recording HD videos.
Camera
With the bugs of MIUI camera its not used fully in the Redmi. Moto lags behind in the segment. Its got a FF camera of 5mp with is *good* just for casual shots. Redmi's Camera is a 8mp can shots pretty good, I mean far better than a Samsung Grand but HD videos make it come down to earth.
UI
Plain Vanilla Android experience can only be accomplished by Moto. Its already got and update of 4.4.4 and will receive a L update AFAIK, the UI is almost bug free and has better RAM management. MIUI struggles even with a GB of RAM, it just provides 400 mb of RAM for free. MIUI has its own UI crash and Camera APp crash issues, for a guy with a first Android phone its not good at all.
Storage
Moto struggles on a 1.66gb of free space to install all your app, but after rooting SD card can be used.Moreover, moto e doesn't has OTG support. On the other hand, Redmi wins the show with about 6gb of Space free and support OTG(correct me if im wrong).
Screen
Redmi wins again. Boasting a 4.7" 720p HD display with 326ppi its spits on the Moto witch has 4.3" display with 256ppi. Both of them bieng equally good Moto had better brightness and saturation levels.
Verdict
Redmi costs about 6k and Moto e costs about 7k Redmi wins Camera, Storage and Screen. However, MIUI has a lot of bugs and a simple SW update cannot make its RAM more free as MIUI will remain resource hungry. And getting it is a pain in the @$$.
If you are looking for a good phone from reputed brand and future Android updates with a bug free day-to-day rugged phone Moto E is for you.
And if you are happy with Indian Brands and want to give Android One a go then you can consider that too.
But IMO Redmi is never recommended.
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For more Info read some Flipkart comments and Reviews on the internet.