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No drawbacks to crossover except increased stress on the frame laterally. Make sure you have the bolt on brace if you do it.
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Not quite correct. Cross over will also give you bump steer. The more angle in the drag link (straight line from pivot to pivot), the more bump steer you will have. But without hydro assist to take the stress off the box, I agree on the need for the brace at a minimum.
Cross over is generally only going to help when dealing with steering while crossed up. The stock drag link it to short for the amount of axle movement we tend to want. So, when the driver's tire droops way down, the drag link gets more and more vertical. This results in less steering range (angle side to side), more difficulty turning the wheel, and more stress throughout the system (including breaking the box off the frame). Cross over corrects this by making a much longer drag link so that for the same amount of droop, you don't pick up much angle. But you do get some angle, even on straight compression and rebound (such as crossing a dip in the road) which is exactly what leads to "bump steer". There is no change in mechanical (or otherwise) advantage, so the ability to steer is not changed except in the crossed-up scenario.
Hydro Assist is completely different. It makes it possible to steer when you have large tires (especially with front locker) without needing arms like Popeye. That's it, it's just more power for your power steering. Rate of steer is a function of fluid flow, ram travel, and ram diameter (basically, ram volume). Power and rate are inversely proportional, so more power means slower steering, all things other than the ram remaining the same.
The only connection between the two is that IF you have Hydro Assist, THEN you better have cross over steering first. This is because traditional steering limits the range (angle) of steering when the drivers tire is compressed/drooped. But the ram, mounted to the axle, could not care less about the range of motion allowed by the draglink/box, so it will try to keep pushing till it reaches its normal limits way beyond what the angled drag link will allow. The relief valve will keep it somewhat in check for a while, but eventually something is going to give, probably the frame…