I think this thread warrants a detailed comparison.
Performance throughout their careers
------------------------------------------
Let's compare their cumulative averages:
First 25 tests: Lara=56, Ponting=40
<b>First 50 tests: Lara=51, Ponting=45
First 75 tests: Lara=48, Ponting=56
First 100 tests: Lara=52, Ponting=58</b>
First 125 tests: Lara=53, Ponting=57
After 131 tests: Lara = 53, Ponting=56 (Lara retired)
As you can clearly see, Lara was the best batsman in the world in the first half of the 90s. He had a dream start but his average fell from 56 to 48 in the next 50 tests that he played from the mid 90s to early 2000s.
From Jan 1 1996 to Dec 31, 2002, Lara just averaged 44 in 55 matches.
He had another peak from 2003, averaged 60 in 41 tests which brought his average back to 53 when he retired.
So, the argument that Ponting had a peak when all ATGs retired or were in their twilight years apply to Lara's 2nd peak as well.
However, like most batsmen, Ponting had a slow start then he hit an astounding peak after that he had sharp decline which lowered his overall career average.
Lara, on the other hand, had a phenomenal start, hit a rock bottom in the middle and then had another peak before he retired.
Consistency
-------------
Now, let's take the series in which they averaged 50+. Lara did so in 17 of 39 series, Ponting did it in 25 of his 59 series.
The ratio is 0.43 which is about the same for both batsmen.
Now, let's take the innings in which Lara scored a 50+ score. He did so in 82 of his 232 innings that is in every 2.8 innings.
Ponting did the same in 103 of his 287 innings that is in every 2.8 innings.
Again, the ratio is about the same.
Interestingly, the ratio for this innings in which they scored less than 30 is also about the same which is in every 2nd inning.
Performance against top bowlers of their time
---------------------------------------------------
One more thing to notice is that if Ponting never had to face Warne and McGrath then Lara also never had to face Ambrose and Walsh.
Against Wasim, Waqar, Shoaib, Ambrose, Walsh, Donald, Pollock, and Steyn, Ponting averages 51 in 42 matches.
Against Wasim, Waqar, Shoaib, Donald, Pollock, McGrath, and Warne, Lara averages 44 in 51 matches.
Performance in Countries
-----------------------------
The 3 worst countries for Lara were 33 in India, 37 in NZ, and 42 in Australia. Lara averages 50+ only in WI, SL, and Zimbabwe. Lara averages less than 40 only in India and NZ.
The 3 worst countries for Ponting were 26 in India, 31 in Zimbabwe, and 42 in England. Ponting averages 50+ in Australia, NZ, Pakistan/UAE, SL, and Bangladesh. Ponting averages less than 40 only in India and Zimbabwe. Note that Ponting just played one test in Zimbabwe.
So, in most of the countries, Ponting did better than Lara.
Conclusion
------------
Ponting did better than Lara in the same number of matches that Lara played. However, Ponting had one of the worst terminal declines which took his average from 58 to 52. I think in ODIs, Ponting was comfortable better and in tests, he was as good as Lara if not better. So, that makes him a better overall batsman for me.