I currently have a Galaxy S3 with a broken screen and LCD. To fix it will cost £160 - £170. If I trade it in I can get £80 - £100. I can't afford a replacement S3 so I am looking at either Nexus 4 or Optimus 4x hd. I am buying a used phone and these are both a lot cheaper than S3,

Does anyone know which is best of the two? I only use it for browsing internet, a little gaming and watching Youtube. (also the occasional phone call)

160 quid is like the official price. Most third party phone shops can do it for around 50. You can buy the glass for around a tenner on eBay. There are videos on YouTube how to do it.

A friend of mine got 200 for her cracked s3 from cpw or p4u I forget which was used to buy her out of her contact 8 months early.

That price is just for the screen but the LCD needs replacing which is what costs the extra plus reduces the price for selling. Sorry I didn't explain it to well in first post

Nexus 4.

So these are the two phones you've been offered with the trade-in of £80 or so? How much real cash are you paying or is it a contract? Sorry, I'm confused - what I'm getting at is if you have a set budget and get the trade-in independent of buying a new phone you may have other options? For example, a new 16GB Moto G is £160 which if you can get £80 for your S3 is an outlay of £80 for a capable new phone.

Given the choice of the two, though, Nexus 4.

I will have about £160 to spend. I have looked at Moto G but think the other two seem to have better specs although I am not great on technical stuff

OK - I guess it depends on whether the Nexus 4 comes with a warranty/guarantee if not new. If so, the Nexus 4 is a worthy contender for your money.

But at least the Moto G will be brand new. And Tesco are selling the 16GB version for £129 (less £10 new customer discount).