Lara: 1125 runs against SL at 86.53 in 8 matches.
Fleming: 946 runs against SL at 72.26 in 9 matches.
Lara: 706 runs against SL in SL at 100.85 in 4 matches.
Fleming: 104.71 runs against SL at 104.71 in 5 matches.
Lara: 419 runs against SL in WI at 69.83 in 4 matches.
Fleming: 213 runs against SL in NZ at 35.50 in 4 matches.
The only years they both played against SL...
1997
Lara: 120 runs against SL at 30.00 in 2 matches.
Fleming: 112 runs against SL at 37.33 in 2 matches.
2003
Lara: 299 runs against SL at 149.50 (including a double hundred) in 2 matches.
Fleming: 376 runs against SL at 188.00 (including a double hundred) in 2 matches.
Both improved their game dramatically during the tests they played as captain.
Both have drawn 3 matches and lost 3 matches to SL. Fleming has won 3, Lara has won 2.
In matches won, Fleming averages 91.00 and Lara averages 31.33
In matches drawn, Fleming averages 147.33 and Lara averages 85.75
In matches lost, Fleming averages 23.33 and Lara averages 114.66
Interestingly, in first tests played in a series, Fleming averages 170.25 in 4 tests - Lara 74.83. Both drop their game for the second test, Fleming with 26.28 and Lara (still strong) at 65.00, and regather for the third test (when played) with Fleming on 40.50 and Lara 175.50
Murali has taken the wicket of Fleming three times in nine tests. He's taken the wicket of Lara five times in eight tests.
There's no way I'm going to try to find out the ODI information, someone else can do that.
Maybe I'll look into it later. It's notable though that Fleming averages 21.53 (27 matches, 560 runs, HS 77*) against SL while Lara manages 52.71 (23 matches, 1107 runs, HS 169). Lara dominates Fleming notably when it comes to playing SL in general. Doesn't change much when you take it from 01/01/2000 either - Lara at 56.80 and Fleming at 24.33.
From this information alone, I'd say Fleming has a very fine edge over Lara when it comes to playing Murali in tests, while Lara is a far, far better batsman in ODI's. Overall? Lara. The test choice is debatable but the fact that Lara is so much better in ODI's shows that Lara is, on a whole, a far more capable batsman against both Murali and Sri Lanaka.
I'm such a factual person.