I don't see the need for cordless, sort if you don't have electric in the field the welder will not do you much good.
Having had both, I'm here to tell you cordless is SO much better.
Up in a lift, inside a tank, or just only having one outlet available. I made do with corded for years, and now, we never touch the corded sharpener.
Same for angle grinders. Now that I have my cordless Metabos, we only use the corded ones if we have a lot of cutting or metal finishing to do. Nothing beats a corded grinder for heavy work, but the utility and convenience of cordless is so good now it's hard to deny.
I have enough cords and hoses to deal with in the field. Taking one or two out of the equation is very nice. Just on the welder alone we have power in, gas in, purge line, ground and torch leads. That's five lines to trip on and deal with for just one machine. Now get the portaband, a tube sander or maybe a grinder, work lights, you name it.