These are listed as managers who have been in charge for at least a half a season. Bearing in mind some have had success in the second tier I would say Sir Bob's record overall being entirely in the Prem is the best overall.

Numbers are games played then win %

Best seven.
1.C.Hughton 64g 59.38%
2.Rafa 63g 57.14%
3.K.K. 251g 54.98%
4.Sir Bob 255g 46.67%
5.G.Roeder 72g 45.83%
6. A.Cox 169g 44.97%
7.G.Souness 87g 44.83%

A big 5%+ difference between the best and the worst.

Worst ten
1.K.Dalglish 78g 38.46%
2.A Pardew 185g 38.38%
3.J.Smith 121g 36.36%
4.I.McFaul 149g 34.9%
5.R.Gullit 52g 34.62%
6.S.Allardyce 24g 33.33%
7.B.McGarry 110g 31.36%
8.J.Charlton 48g 31.25%
9.S.McLaren 31g 22.58%
10.O.Ardiles 47g 21.28%
An honorary mention to Joking Ear with 18 games and win ratio of 22.22% (would have made 2nd worst)

No doubt it would be interesting to see how they compared considering the amount they had to play with adjusted to today's values. An impossible task I would think