Karth/Offizer
They are not the greatest regiment of all time in terms of skill, but I'd say their leaders might be. Even with low melee skill the 63e can dominate other regiments as the leaders pretty excellent tactically.
Tico/Breaches
These guys held the spot of best regiment for at least 3 years straight. However they always have had some of the best meleers in the game, so we don't know what the regiment might have been like with less skilled melee. Because of that they are slightly below Karth/Offizer.
AsianP
Old school leader known universally, every regiment he leads will compete for top 3 regiments, and has held top 1 most notably during the 79th days. Has always had some of the best melee players in the game, so like Tico+Breaches, I put Asian below Karth.
Grimsight
Lead only contending regiment against the 12th during their reign. Pioneered some new tactics that you see used in every 1v1 these days.
CheeseyPants
Cheesey lead his regiment to be the top regiment for a short period of time and won Season 3 NWL. However things slowed down after some key melee players went inactive/left.
Lawbringer
Lawbringer created a very serious contending regiment, springing up almost out of no where. They did well under his leadership, I would note that they had some very very good melee players to rely on however (Many of their regulars came from a native clan)
Alexander
Won the TNWL with some great leading. Would have to see them reign longer to be higher on this list though.
Stox
Stox wasn't very interested in competitive linebattle, it was more Locust & DrBYeByes doing. Regardless they did quite well in 1v1s. Note that they did have a huge amount of players to choose from for their 1v1s.
Millander
One of the great leaders of the early days of NW, and lead the guys who created the 9y. However there wasn't as much of a focus on 1v1s so we can't know how he would do these days.
Ody
Through all the hate he gets, hes a decent leader. Crutched on melee during some periods though.
