I'd say on the batting there that's very debateable - especially over the 2003-05 period when he was at his best with the bat.
Excuse the late reply...
You're right, Flintoff was consistent in that period, but still don't think he ever had as consistently good a series with the bat (against quality opposition) as Cairns did in the low scoring but competitive 3 test series against Aust in 1999-2000
Results | Global | Cricinfo.com Flintoff went close in the 05' Ashes with 401 in 10 innings (ave 40), but just to provide context on Cairns' effort, his 341 runs in 6 innings was the most runs of batsmen in either side.
New Zealand batting averages Player Mat Inns NO Runs HS Ave BF SR 100 50 0 4s 6s
CL Cairns 3 6 0 341 109 56.83 534 63.85 1 2 0 39 13
CD McMillan 3 6 0 194 79 32.33 419 46.30 0 2 1 30 2
AC Parore 3 6 1 144 46 28.80 374 38.50 0 0 0 14 4
NJ Astle 3 6 0 167 61 27.83 275 60.72 0 1 1 24 0
SB Doull 2 4 1 69 40 23.00 67 102.98 0 0 0 7 2
SP Fleming 3 6 0 137 60 22.83 374 36.63 0 1 0 16 0
CM Spearman 3 6 0 105 38 17.50 303 34.65 0 0 0 14 0
DL Vettori 2 4 1 50 27 16.66 92 54.34 0 0 1 9 0
MS Sinclair 3 6 0 61 24 10.16 157 38.85 0 0 1 7 0
MJ Horne 3 6 0 44 14 7.33 174 25.28 0 0 1 4 0
PJ Wiseman 2 4 0 27 16 6.75 93 29.03 0 0 0 5 0
DR Tuffey 1 2 1 4 3 4.00 24 16.66 0 0 0 0 0
SB O'Connor 2 4 2 6 4* 3.00 35 17.14 0 0 2 1 0
Australia batting averages Player Mat Inns NO Runs HS Ave BF SR 100 50 0 4s 6s
DR Martyn 3 6 2 241 89* 60.25 409 58.92 0 2 0 41 1
JL Langer 3 6 1 288 122* 57.60 330 87.27 1 1 0 37 4
SR Waugh 3 6 2 214 151* 53.50 421 50.83 1 0 0 32 1
ME Waugh 3 6 2 190 72* 47.50 360 52.77 0 1 0 24 1
AC Gilchrist 3 5 1 144 75 36.00 227 63.43 0 2 0 24 1
MJ Slater 3 6 0 177 143 29.50 311 56.91 1 0 0 28 1
ML Hayden 1 2 0 39 37 19.50 67 58.20 0 0 0 6 0
GS Blewett 2 4 0 50 25 12.50 246 20.32 0 0 1 5 0
SK Warne 3 4 0 36 12 9.00 48 75.00 0 0 0 7 0
GD McGrath 3 4 0 30 14 7.50 86 34.88 0 0 0 1 0
B Lee 3 4 1 20 8 6.66 49 40.81 0 0 1 2 0
CR Miller 3 4 0 14 8 3.50 27 51.85 0 0