I can't recall the technical terms right now, but human motion can be divided into two logical groups: Movements that are stable throughout (you can freeze at any point and maintain that pose for some time) and movements that are only stable at the start and end but are inherently dynamic at some point in between.
For instance, when you lie on your back and make snow angels, that's a static movement. You can stop at any point and hold that position. The position may be uncomfortable or exhausting, but the point is that it's possible to hold it all for any time whatsoever.
An example of a dynamic movement is jumping. There are points in the jump where you cannot stop, for instance when your legs leave the ground. Another good example is running or jogging (because there are moments when neither foot is in contact with the ground) but not walking or power walking.
I think with these so called stable movements the exoskeleton could work. For it to feel like Earth, the resistance that a human experiences must be the same. The suit would essentially be applying force defined by Earth gravity vector minus Planet X gravity vector, so it would push upward at all times. It would need a computer to calculate how much force to apply at what joint, but that's relatively easy to do. It may or may not be necessary to "train" the suit to work with that individuals idiosyncratic movements, but I think either way is plausible.
You would probably have a range of suit qualities, with the worst being just a bunch of bare bones struts, while the best ones distribute the force more evenly on the human body, but in principle the main force that the human must apply can be made to exactly equal that which would be needed for the same movement on Earth. Secondary forces might be harder - for example if the suit is poorly constructed, there may be an excessive strain on smaller balancing muscles which resist the heavy gravity dragging the human out of the suit harness in certain position. You might make a plot point out of lower classes from Planet X having distinct but subtle muscle hypertrophy in certain unusual areas, similar to many occupational diseases associated with excessive strain on a certain part of the body.
Where this illusion of Earth gravity falls apart is the dynamic portions of movements. For example, the suit could provide a walking experience mimicking Earth, but it cannot mimic a jump. The reason being that once the jumper is airborne, a purely mechanical suit no longer has a surface to press against to apply the counter-gravity force. The motion of the jump may feel exactly like Earth, but as soon as the subject leaves the ground they will obviously fall faster than on Earth. Also, when the suit wearers step on flexible objects that they "know" would support their weight on Earth, they might be surprised to find out they are easily crushed (which could be another plot element concerning novice or careless users).
With a bit of thought you will observe that dynamic movements are very common in every day life. Besides running, sitting down, getting up from a prone position, quick turns and going up or down stairs can all have dynamic component. It might make the suit very startling to wear, since unless you are carefully trained in its limitations, you will often be surprised by abrupt and unexpected losses of antigravity force. Suppose you descend a familiar stair for the 100th time, but this time get overconfident and careless and let go of the banister - but instead of being slightly harder like you expect the movement is suddenly 10 times harder. Probably after a few weeks or months the human brain can adjust to it, but if a person wearing the suit for the first time is careless they can easily get injured or killed. The experience of learning to use the suit would probably be somewhat analogous to learning how to ice skate - while in principle it is not very hard, you do have to learn to cope with the fact that you are suddenly much more stable in some directions (left-right) and much less stable in others (front back).
If your suit is not actuated solely by mechanical means, you could correct the dynamic motions as well. One obvious way I can think of is to attach tiny jets or rocket thrusters to various limbs. You would have to carefully watch your fuel, since when it runs out gravity will suddenly increase (or perhaps the suit detects low fuel and starts gradually reducing thrust to avoid surprising you) and you could be hurt. Alternatively, some sort of magnetic shenanigans (perhaps magnets in the hip repelling magnets in the arm or something like that) could correct gravity for some dynamic motions, such as "collapsing on the couch", but probably not ones requiring loss of contact with the ground unless you want a magnetic levitation kind of technology.