I don't think there is a "best" Android phone out there right now, because everyone has slightly different needs and all the top-tier phones have pluses and minuses. For example...
Galaxy S3: often held up as the de facto standard for what a non-Google Android phone should be, but the processors used in the various versions are no longer top of the line. The OS is heavily skinned, and the phone is almost a year old at this point.
Note 2: checks all the boxes when it comes to features, and probably has more functionality than any phone on the market (of any OS). However, it's very large, few apps outside of native apps take advantage of its capabilities, and the OS is also skinned heavily.
Nexus 4: pure Android as Google envisions it. Top of the line hardware at a crazy price, but lacks sanctioned LTE and some features that many people love, such as an SD card slot and removable battery.
Droid Razr Maxx HD: best in class battery life, supports many desired features like expandable memory and LTE, good hardware overall, but locked to a carrier with a very checkered history of updates.
These are just my observations. Some won't see the negatives as such, and some may not see the positives outweighing a particular negative. If you want a pure Android phone that will get timely, bleeding-edge updates, then the Nexus 4 is your best bet. If updates are not all that important to you, and you want LTE, then no, it's probably not your best bet. For me, it's perfect.