The Note 3 is a fantastic phablet. Not as good as the new Note 4, obviously, but still very good and should last a few years for the average user. The S4 is also a great choice if you want a smaller phone. People rag on Samsung for their massive amount of bloatware installed on the devices, but once you get rid of them the devices themselves are fantastic.
The Nexus 6, if it is within your budget, is looking to be a very stellar device and should compete with other current flagships, such as the S5, the Note 4 and the LG G3, as well as the HTC phones which I'm not as familiar with. Very solid choice, and running stock Android 5.0 is a big bonus.
There's not going to be any consensus "best" Android smartphone, because diversity and a plethora of options is one of the main selling points. It's going to come down to your preferences, really.