You are getting some good advice here but I would like to clarify a couple of things and also make some suggestions:
First - get your hands on a copy of the digital manual and familiarize yourself with it. It is long but chock full of great information. It is thorough and provides sound general detecting advice, regardless of whether you are using an Equinox. However, if you do nothing else, at least familiarize yourself with the mode descriptions and what they are optimized for.
Second - The 800's 8 modes (yes, eight different modes, not 4) are essentially like having 8 detectors built into one machine. The thing that is different about Equinox is that the "local" parameters for those modes have to be set separately for each mode just as Steve pointed out. The only "Global" settings are Sensitivity, Volume, and Backlight. Threshold is Global for Park, Field, and Beach modes and Gold Mode has its own Threshold settings. Each mode uses a different frequency spectrum (combination of the fundamental frequencies) and different target signal processing. It is the combination of frequency spectrum and signal processing that defines the Multi IQ secret sauce for each mode. That is why you can have two modes set up exactly the same in terms of tones, recovery speed, iron bias, etc., yet each of those modes will behave differently with specific targets. Also, Multi IQ does not just affect target recognition but is fundamental to how how the machine ground balances and also means that each mode will be more or less susceptible to different types of EMI so you must noise cancel (with coil off the ground like an antenna) and, if necessary, Ground Balance for each mode. Now once you have noise cancelled and ground balanced for a given mode at a site, you do not generally have to go through that again every time you switch modes. Let your ear be your guide, if you are hearing interference, then by all means attempt a noise cancel again. If that does not fully take care of the problem then you can lower sensitivity. The machine is plenty sensitive, so don't be shy about lowering sensitivity to get rid of chatter. The machine, due to Multi IQ, is very forgiving for a less than perfect ground balance. It doesn't hurt to do an Auto GB just to be sure, but the way you know if you need to do it is if you are getting a lot of ground chatter that sounds like iron feedback (grunts and -8/-7 bouncing VDI's) when you press the All Metal button. This machine is all about getting the noise out. Running it quiet and maximizing Signal-to-Noise ratio, not just driving the signal high (e.g., maxing out on gain).
Third - Quick Mode Summary - In general, the "1" modes for Park and Field are weighted to the lower frequencies of the spectrum and are, therefore, more sensitive to high conductors like pure copper and silver and to larger sized targets overall. The "2" modes for Park and Field are weighted to higher frequencies of the spectrum and are, therefore, more sensitive to mid-conductors like aluminum, zinc, gold, brass, small lead, and smaller-sized targets (the higher frequencies can better resolve the smaller targets) like jewelry, buttons, and pieces of metal like earring backs and percussion caps as well as annoying targets like small pieces of foil or wire. The Beach modes are designed to be able to balance salty, wet ground and are also more sensitive to high conductors. Beach 1 - dry/wet sand and Beach 2 - wet sand/surf. Beach modes probably use the lowest frequency weightings and hat sounds like a great silver sniffer but Beach mode also dials back transmit power if it senses high mineralization (such as black sand) so is not something you want to routinely use off the beach (Beach mode also cannot be run single frequency). Finally, the Gold Modes are very different than any of the other modes because it uses VCO audio which varies in pitch and intensity based on proximity to the target, they also use the highest frequency weightings of any mode and are primarily for prospecting small natural gold. Gold 1 for "mild" soil conditions and Gold 2 for high mineralized soil (which is typically where natural gold resides). Gold mode may also be useful for relic hunting in high mineralized conditions because many relics are also mid-conductors (brass, small lead). As is true for most detecting "rules", there are no "rules". Nothing says you can't use Park mode on the beach, for instance and in some cases, that might be a good move. Park 2 as well if you want to up the gain on gold jewelry in dry sand for instance. Also, do not be afraid to stick with one mode for most of your detecting needs (e.g., Park 1). Since all the modes use Multi-IQ you should not necessarily be completely shut out from detecting just about any type of metallic target regardless of the frequency weighting.
Fourth - What you were seeing with that dime - At the highest level, based on mode behavior, I would expect that Park 1 might hit harder on that dime than Park 2 but not to the point that you could not get a decent VDI at 6". Steve may be right in that there may be something else in the proximity of the dime that is overriding the the dime signal because of Park 2's increased sensitivity to mid-conductors, but I find it hard to believe it would be that radically different. Two thoughts - you may indeed needed to do a ground balance in the Park 2 mode but it doesn't seem likely that would be the cause of the issue. You may have also inadvertently changed some settings in Park 2 that affected its performance. I suggest that you do a Factory Reset of the machine to get everything back to ground zero. If you want, you can just individually reset the Park 2 mode. If you do a factory reset, you will need to re-pair your wireless phones. Once you have all the settings back to their defaults, re-run your test, but this time do it with the ALL METAL (Horseshoe) button pressed to suppress any discrimination and to eliminate discrimination filter effects. This will also enable you to hear the presence of iron in the hole that may be having more effect in Park 2 than in Park 1 (Park 1 also has relatively high default Iron Bias setting, but this should only really effect iron falsing, plus Park 1 was not giving you any trouble on that dime).
In any event, keep these things in mind overall as you learn the machine - 1) Get it running as quiet as possible - Noise Cancel, Lower Sensitivity, and GB if necessary (need to do this the first time you use a mode at a site). Recovery speed also has an effect on ground noise depending on your swing rate, so be conscious of that and don't just lower recovery speed to gain raw depth because you may end up just increasing the noise floor similar to unnecessarily increasing sensitivity much above the default of 20. Also - make sure your cell phone is in airplane mode or at least not in a pocket that is close to the control head of the detector. 2) Until you get really comfortable with the machine, stick with one or at most two "Go To" modes so you can get used to the tones and behavior of the machine. Remember that each mode is like a different detector and who needs to be learning more than one detector at a time - avoid the temptation to "Mode Hop". 3) Avoid radical changes to your "Go To" mode's local settings. Get comfortable with the defaults then adjust the defaults a couple clicks to get the desired effect. 4) Have fun and go snag some keepers!
HTH.