This... This is one interesting question! Well, Let me get started!!
Alright, So when Halo 3 had come out, Forge was more of a small tool; Something to use to edit the weapon layout and or spawn points. But after Foundry had come out, People in the community went in and made these amazing maps! Alexo670 with his shopping mall... Arby n' The Chiefs very own wedding episode... All in all, Forge was becoming something that people loved - And Bungie kept their eyes on that and made sure that it was maintained... Creative!
And that is when our very beloved map Sandbox had been aired to the gamers, And sure enough we had a huge assortment of pieces to use and mess around with. Like Arbiter 617s Pizza Delivery machinima, Located in a city built entirely out of the worn our sand blocks and wedges of the Sandbox. And that is when forge for Halo 3 met its limit.
When Halo: Reach had come out, It had brought forge back into the welcoming arms of machinima directors, builders, clan leaders, and just over all the fans a like. Halo: Reach had welcomed Forge World, A blank canvas for us all to use and let our minds flow. Reach had also welcomed new types of pieces... New inclines, New tunnels, New walls... New everything actually! And with the new "fine editing" tool, It made building your dream maps so much easier. Many famous games were either made or re-made in Halo: Reach! Like Speed Halo, Ice Cream Man, Fat kid, Etc.
When Halo 4's forge had been brought to the table, It was actually a different situation. We now had dynamic lighting, Welcoming some new shadows for the lovely and talented lurker Azaxx to roam in. And though Halo's forge pallet had a bunch of white foam looking items, And a more UNSC directed arsenal of objects, (Oppose to Halo: Reach's Forerunner look, And colors)... Halo 4 welcomed in magnets, Which could be a nuisance every now and then, As certain pieces don't fit correctly. 343 had also brought in duplication, A fast way to set options on items and keep them like that, With the click of one button. Halo 4 had 3 individual forge environments, Ravine, Impact, and Erosion. Erosion having its own Grifball court as a bonus... But since some fans didn't like the lack of area to forge, 343 released Forge Island, 3 different islands, 3 different sizes, and more objects to use. Also a green screen for some of those machinima directors as well.
All in all, I think (In my opinion) that Halo: Reach's forge mode had been the best. Though it doesn't rival Halo 4's Magnets, Dynamic Lighting, and duplication, Halo: Reach had a more vivid look to its items, Instead of a foam look. Halo: Reach also had more than just UNSC created items, Featuring covenant crates, gravity lifts, and objects that appeared more forerunner than anything! Halo: Reach also had Forge World, Which had a good balance between land and water, Making it possible to connect your fort to the island, or blood gulch. Also, You can't just leave out the colored Mongooses either!!
That is my view on it, Thanks for reading!! - TDM