I would advise against the Galaxy Nexus. I had one and sold it a few months afterwards.
It was a nice phone n all and the screen was vibrant but here are some of the things that I didn't like about it:
1) Camera sucked. If you're used to the 8MP shooter on the back of your 4S then you will notice a significant drop in quality.
2) Speaker sucked. The speaker was very quiet and got distorted at near-to-max/max volume. The speaker on the 4S is much better than the speaker on the Galaxy Nexus. I would often miss calls when walking outside with the phone in my pocket due to this issue.
3) Text wasn't as crisp as the iPhone 4/4S/5
4) I felt the hardware was a bit under powered for the 720p screen. I found it lagging at times even on 4.1.
5) My BIGGEST issue and one that is overlooked by many people was the sound quality through earphones. I'm really into listening music on my phone as I walk outside. The DAC quality on the galaxy nexus is hands down, terrible. The loudness and quality of music coming through the phone and into my earphones was just downright awful.
Take a look here for more information -
http://androidforums.com/samsung-ga...s-galaxy-nexus-sound-quality-vs-galaxy-s.html
Pulled from above link -
"I used the same FLAC files to play in the stock Galaxy S and Galaxy Nexus player to do a comparison.
This will not be a long post. Simply because the Galaxy Nexus' sound quality is very poor in comparison to a Voodoo'ed Galaxy S. In technical terms, the treble and bass are very roll-offed. This means that the audio chip does not reproduce the highest and lowest frequencies of the music sufficiently. Also, the soundstage is compressed and for some reason the tonality is off. I have no idea why it can sound that bad but it does."
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It is for these reasons that I recommend you don't get a Galaxy Nexus. Since you mentioned that you are on a budget, I think a Nexus 4 or a used Galaxy S3 will satisfy your budget as well as not having any of the problems I listed above.
The S3 has the added benefit of having a swappable battery as well as having a microSD card slot for your storage needs.