You haven't really stated any requirements (apart from "Like to do more when away from desktop", which doesn't really help much - like to do more Large Hadron Collider data analysis or more dealing with e-mails...the requirements are so different, it could imply anything).
Anyway, the Nexus 4 has the reputation of being good value for what is a high spec phone. I understand that LG's phones don't really have the best of reps for the things like build quality and appearance, but the N4 isn't wholly an LG design. That said, I haven't held/used one (they may have caused quite a stir, particularly with the pricing, but they aren't all that common on the streets here), so it might not be the best package, I can't tell.
The Samsung is probably the safer choice out of those two, but is more expensive (in most of the world, anyway - you'd need to look at local pricing carefully to be sure what was on offer where you are).
What about the HTC One? My opinion is that is the more attractive looking package (but is probably too new to be available at bargain prices yet).
And, what about lower down the price scale; is there any reason that a cheaper device won't fulfil the requirements?