What is the general thought about the Brewer's Best Deluxe Equipment Kit? I am able to purchase a slightly used kit at a reduced price. It this quality equipment or should I go with the kits from Midwest or Northern instead?
If it has a carboy/bucket, a brew pot, funnel with filter insert, tubing for blowoff and siphon, an airlock, bungs for carboy/bucket, hydrometer, etc. go for it. That's pretty basic, fundamental stuff. Things other than those listed above are just bonuses. BTW, post a link to whatever you are talking about to get a more detailed response from somebody.
I haven't really bought too much brew equipment (since I got this as a gift) but the wort chiller and the large pot are awesome. I have no complaints with the set.
Most of the fundamental brewing kits have the same things. I started out with the same Brewers Best Deluxe Kit and liked it a lot. It has held up for years and I am still using all the equipment. There are small differences in each, but generally all comes with the same type of pails. Williams is a little different because their ale pail is 'siphonless.' Basically it has a valve at the bottom of your primary pail so you don't have to siphon.
Whatever you decide, I would add two things. An Autosiphon and a better book (how to brew by John Palmer and The Complete Joy of Hombrewing by Charlie Papazian.)
Remember too, it is more about your brew processes than the equipment. There are folks on this forum that make top notch award winning beer with the basic kit.