zone.utcOffset(timestamp); // 480

Get the offset for a given timestamp (in milliseconds) from a Zone.'America/Los_Angeles').utcOffset(1403465838805); // 420'America/Los_Angeles').utcOffset(1388563200000); // 480

POSIX compatibility requires that the offsets are inverted. Therefore, Etc/GMT-X will have an offset of +X and Etc/GMT+X will have an offset of -X. This is a result of IANA's Time Zone Database and not an arbitrary choice by Moment.js. Thus, using locality based identifiers is preferred over fixed-offset identifiers.

This is also described on the Wikipedia entry for the database:

The special area of "Etc" is used for some administrative zones, particularly for "Etc/UTC" which represents Coordinated Universal Time. In order to conform with the POSIX style, those zone names beginning with "Etc/GMT" have their sign reversed from the standard ISO 8601 convention. In the "Etc" area, zones west of GMT have a positive sign and those east have a negative sign in their name (e.g "Etc/GMT-14" is 14 hours ahead of GMT).

For example, using the Europe/Madrid identifier gives a different result from Etc/GMT+1.

moment().tz('Etc/GMT+1').format('YYYY-MM-DD HH:mm ZZ');
// '2014-12-18 11:22 -0100'
moment().tz('Europe/Madrid').format('YYYY-MM-DD HH:mm ZZ');
// '2014-12-18 13:22 +0100'