Both are great platforms - and you are in the right place for great opinions!
If you were going with a mild build (not going with larger tires or full set of bumpers, sliders, and skids), I think the GX, with lower mileage, makes a lot of sense.
That said, if you are going with a larger tire that will not fit in the factory spare location of the GX460, the next step is a hop down a rabbit hole of more weight, more compromises, and more $, and you wind up with a vehicle that might have a little more ground clearance than a mild LX, but you have less power, equally terrible (or potentially worse depending on the build) mileage, and less space. Please don't ask me how I know about this rabbit hole, the mpg, or the lack of power in the mountains

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Yes, the LX is heavier to start, but it has more space inside, more power on the highway, and you can fit a larger tire in both the wheel wells and the factory spare location. You also have larger differentials, beefier CV's, a larger steering rack, thicker tie-rods, etc. While the payloads are within ~ 100 pounds for a given year, based on both the size of key components, as well as time spent driving factory *ish spec 150 and 200 series vehicles as well as those on 33 and 35 inch tires, I think the LX will handle the weight and larger/heavier tires better.
Side-note for posterity - lest anyone think I am not a fan of the 150 series platform, I really like them and think that the GX is a great package and size for a daily driver you can wheel on the weekend. In fact I like them so much that I actually looked at the parts and options to swap in a Tundra/LC200 front clip to a GX460 to get the larger differential, steering rack, etc (similar to what Arctic truck did with a few of their truck builds). But by the time I tallied up the cost of the front clip swap and a larger rear axle it made more sense to go with an LX or LC. For better and worse, with sliders and an oil pan skid I think that both vehicles almost always run out of clearance on tight trails before they run out of capability.