I recently took some time to compare the differences in damage output between Ifrit's Cudgel, which I recently received, and my old Lightning Brand (single melded with INT+17).
Let's start by looking at the stats on these two items:
Ifrit's Cudgel
Fire Resistance +15
Attack Magic Potency +30
Chance to inflict Fire damage.
Lightning Brand
Attack Magic Potency +20
Lightning Magic Potency +10
Lightning Resistance +10
Intelligence +17 (from single meld Tier IV materia).
Now, we've been told that the intention is for raid equipment to outclass single-melded equipment of its level, but not double-melds or higher. Of course, this is an ambiguous generalization that will likely fail to apply in every circumstance.
My intention with this post is to compare damage when casting "Thunder" with the equipped weapons. Additional tests will be run at a later time to determine the effects when casting other spells, and how much the resistances come into play. However, since the goal of most thaumaturges in parties seems to be the casting of the "Thunder/ara/(aga)" chain of spells, I've decided to focus on this first.
The Setup
I chose to test against Molten Mitelings, found near Nophica's Wells. I took care to make sure I got data from an equal number of level 30, 31, and 32 mitelings, so that the averages would be more accurate when comparing damage. My sample size was relatively small, though not insignificant - I tested against 99 mitelings total for each weapon (33 of each level).
Care was taken to ignore critical hits, as these were special occurrences that would affect the results. Whenever a critical hit was scored, I ignored the result and retested against a miteling of the same level. The same care was taken to avoid damage that was resisted, although no hits were resisted by mobs of the level tested against.
The Data
After collecting my data, I averaged the damage dealt across each of the three levels of mitelings, and came up with the following numbers (these are averages, as level of each monster was tested 33 times for each weapon).
Ifrit's Cudgel
Miteling Lv. 30 1402.15
Miteling Lv. 31 1341.62
Miteling Lv. 32 1192.08
Lightning Brand (Single Meld, Intelligence +17)
Miteling Lv. 30 1440.77
Miteling Lv. 31 1386.38
Miteling Lv. 32 1356.69
The Results
By taking the above data and averaging it across all three levels tested, we can get our final numbers for the damage output (when casting "Thunder") of each weapon.
Ifrit's Cudgel
Avg. Damage 1311.95
Lightning Brand (Single Meld)
Avg. Damage 1394.61
Lightning Brand (Single Meld) wins out here, with about a 6% greater damage output over Ifrit's Cudgel.
This data would seem to suggest that if your goal is to have the highest-damaging Thunder, Lightning Brand with an Intelligence (Tier IV) meld would be your best bet. A double-meld should fare even better, and I am very interested in testing such a weapon further.
Please keep in mind that the implications of these results are very limited in scope, and that further testing is necessary to come to a completely conclusive result.
The Future
My future tests will pit these items against each other while casting spells of the non-Thunder variety, to see what the benefit overall would be. I'd also like to run further tests using "Thundara" and "Thundaga", and against different enemies, including those weak or resistant to the elements.
I will upload more data as I collect it in the near future. If anyone has any additions or suggestions, please comment below.
tl;dr: Lightning Brand with a single Tier IV Intelligence materia meld seems to be more potent than Ifrit's Cudgel when casting "Thunder".