(1) Both instruments are meant to replicate a factor of the daily movement of certain instruments using a variety of leveraging techniques, including derivatives.
The fact that they are shooting for "Daily" 3x movement and not something on a larger time frame suggests that these are not good "investment" vehicles, although I can see people wanting to dollar cost average in NUGT small and over time to take advantage of splits the underlying undergoes from time to time. My guess is that, intratrade, you'd be in for a "rough ride" if you want to play these that way.
(2) The instruments and derivatives being utilized on any given day are somewhat "opaque." In other words, these funds' managers do not use a single index, instrument, or underlying, but may be using multiple underlyings and different derivatives of those on a given day to achieve fund goals. This is in stark contrast to an instrument like VXX , which is a derivative of a single instrument and where a direct and useful relationship can be drawn between current VIX "spot pricing", the pricing of VIX in front months, and the existence of states of contango and backwardation that can form the basis for actionable trades.
(3) Because of this feature of these particular funds, it is basically impossible to cleanly or precisely chart a direct relationship between gold prices and these instruments. However, NUGT will move "generally" down when gold prices move down; DUST will move up. However, they will not necessarily move 3x the movement of gold , as the fund names suggest. They may move more; they may move less. (Friday, for example, XAUUSD moved down 2.47%; NUGT moved down 24.52%).
(4) Because these funds' managers use derivatives to achieve fund goals, both of these funds appear to be subject to contango and backwardation (See Split History). NUGT price, over time, naturally declines with this effect; DUST, increases.
Because of this, my tendency would be to trade these instruments with "the contango flow", buying NUGT or taking assumption trades on "meaningful dips" and selling DUST on "meaningful rips." Although my take on these instruments is that they are meant to be "traded," rather than "invested" in, it's entirely possible for you to get caught in a trade longer than you would like. In that event, I'd rather be on the side of contango drift ... .
For this reason and in spite of the fact that these instruments do not enjoy a direct, clean relationship with spot gold prices, I would nevertheless look at spot gold prices and price action before initiating a trade in either DUST or NUGT , as opposed to using these funds' price action to initiate a trade. This approach would be similar to my trading of VIX derivatives where I don't look at the price action of VXX , for example, to enter, I look at VIX instead in inform my entry.
Next: NUGT -- Buy Shares or Sell Puts?