Strictly approaching? Lids hand down. You can run the basket from everywhere basically and almost never have a long come backer. The real trump card of the lid is that they're so much easier to land flat or match the slope of the ground and have blunt, skip averse rims so they make approaching risky/fast greens a lot less dramatic. The trad putter or brick have much higher roll away potential, especially the brick.
The advantage of the trad putter is mostly familiarity aka mold minimalism. If you have much range on your jump-putts then you can negate a lot of the advantages of a lid, especially if it's windy.
The advantage of the brick is "Safeton golf" where you can throw easy hyzers all day, either BH or flick. The slow panning FH with an overstable disc like a Zone, A2, etc (Bergs are killer at this) is also a stupidly useful shot. But if you're stuck with a straight at it look, i.e. no hyzer lines, then the brick is sub-optimal.
I bag all 3 of these options though with a Polecat, Keystone, and A2. The terrain in NC can change a lot depending on whether you go East or West so they all get used.