Nothing is ever conclusively proven. Just as I can argue that despite the fact that Ponting did poorly against average bowlers in India; everywhere else and against every spinner he did as good if not better than Lara. Whilst Lara had trouble against the likes of Kumble and Vettori. It's all arguable.
Ponting scored 104 in Bridgetown against Ambrose and Walsh; all his tests against the WIndies they were together and he averages 40 against them.
And 197 against Wasim, Saqlain and a young Akhtar, averages 50 against Pakistan. And clearly played S.Africa well. Still a far cry from averaging 30s, even if you were to add Waqar to that list - who Ponting did actually face later in the 00s in those harsh neutral tests.
Also, how did Lara do against India in India? So even if you want to argue that India in India should count, Lara still only has a solitary success against Australia. Failure against the 3 others. Ponting failed in India, but succeeded against the 3 others. It's all arguable, but IMO that's pretty conclusive amongst greats.
I don't want to harp on the same thing again and again but here goes..
Lara averages something like 36 against Ws including a series (albeit at home) against the Ws at their very zenith and an away series where by all accounts there was so much disharmony within the team that there is no way the man at the centre of it was going to do too much... (See Windies in South Africa in 98 again for the same stuff..) Ponting got 3 ducks and a 197 against an attack with Wasim in it, albeit well past his best.. How is that comparable?
Ponting averages little less than 40 against Windies (Walsh and Ambrose) and against an attack of comparable quality, Lara averages in excess of 50 against McWarne + plus other good bowlers.. The attacks Ponting faced had Walsh and Ambrose and then zilch.
Ponting averages tailenderesque in India where Lara inspite of 30 (one series VERY early in his career, not enough for me, but u keep bringing it up) and even considering juz the 90s (4 tests or something for Ponting) he still averages lesser.
The only real win AFAIC here is against Donald but this is offset by the fact that Ponting has a middling record Vs Windies (late 90s Windies means juz 2 great bowlers followed by buffet bowlers) whereas Lara averages 52+ with a SR of 60+ against the best attack(McWarne juz as dangerous as Ambrose/Walsh for me and Australia EASILY had the better support bowlers) with even less support from his own batsmen...
And I am not even bringing up the off field stuff and the fact that Ponting played in a better team than Lara, which meant most of the time, less pressure on him from a team PoV...