When looking at Amp vs Critical Damage there are two factors to consider to determine which is better, and that is your base value (Attack and/or Magic Attack) and critical rate.
The general order in how they affect your attack power is:
Base attack value +(Base attack value * (%amp/100+1))+ Add attack value = End attack value.
On a critical hit this is a bit different: Base attack value +(Base attack value * (%amp/100+1))+ Add attack value * (%critdmg/100+1) = End attack value.
(IMPORTANT: Base value and Amp, play the most important role against opponents with high defense. Critical damage will only be successfully applied to a target if base and amp values can successfully "break" (or penetrate) the target's defense and resist amp values.)
The relationship between base attack vs. base defense seems to be a 1:1 unit comparison. Where if one value is higher than the other by a large enough margin, one's attack can either be almost totally neutralized, or one's defense almost totally penetrated. Amp and Resist Amp exist to potentially upset this balance.
In an experiment using a level 180+ Force Archer (1100+ magic attack, 50%+ amp, 100% critical damage) against a test level 180+ Force Shielder (1100+ defense, 5% resist skill amp) with level 20 "Art of Defense" skill engaged, the FA's level 20 "Critical Shot" skill (45% magic skill amp, 105% critical damage, 103 add attack) was unable to penetrate the target's defense, and did noticeably negligible damage to the target. When the FA used level 20 "Terra Lance" (95% magic skill amp, 119 add attack) it did noticeably more damage to the FS.
"Terra Lance", a skill with no native critical damage, caused more damage than "Critical Shot" which is a skill filled with critical damage. This occurred because Terra Lance provided enough AMP to successfully penetrate the target's defense. Critical Damage on its own WILL NOT penetrate defense, no matter how much of it is present. High enough Base and Amp is required to penetrate defense. Critical damage exploits the defense breakage, and provides extra damage proportionate to the amount of broken defense.
When the Force Archer engaged Battle Mode 2, all of the skills did noticeably higher damage against the Force Shielder using "Art of Defense", successfully penetrating the defense. This is due to the Base Magic Attack increase from Battle Mode 2. FA critical damage improved.
When the Force Shielder engaged Battle Mode 2, the Force Archer's skill again did noticeably lower damage against "Art of Defense", successfully reestablishing defense. This is due to the Base Defense increase from Battle Mode 2. FA critical damage reduced.
As you can see critical damage is calculated on how amp builds on your base. This is where critical rate comes into play, because you don't land a critical hit all the time the critical damage isn't added on every attack. If you have to decide between, for example, A 7% amp/10% critical damage blade and a 20% critical damage blade it is depending on your base attack power and preexisting amp (amp in armor, accessories, skills, pets, and epaulets) which will be more effective. (If you can get the same weapon with critical rate included, then more power to you.)
NOTE: The following assumes 1000 base attack and 0% preexisting amp.
7%amp/10%critdamage weapon.
| %Crit rate | Base attack | Average %Dmg from amp | Amplified Base | Average %Dmg from crit | End value | Total % average Dmg increase |
|---|---|---|---|---|---|---|
| 10% = | 1000 | *7% | 1070 | *1% | 1080.7 | 8% |
| 20% = | 1000 | *7% | 1070 | *2% | 1091.4 | 9% |
| 30% = | 1000 | *7% | 1070 | *3% | 1102.1 | 10% |
| 40% = | 1000 | *7% | 1070 | *4% | 1112.8 | 11% |
| 50% = | 1000 | *7% | 1070 | *5% | 1123.5 | 12% |
| 60% = | 1000 | *7% | 1070 | *6% | 1134.2 | 13% |
| 70% = | 1000 | *7% | 1070 | *7% | 1144.9 | 14% |
| 80% = | 1000 | *7% | 1070 | *8% | 1155.6 | 15% |
| 90% = | 1000 | *7% | 1070 | *9% | 1166.3 | 16% |
| 100% = | 1000 | *7% | 1070 | *10% | 1177 | 17% |
20%critdamage weapon
| %Crit rate | Base attack | Average %Dmg from amp | Amplified Base | Average %Dmg from crit | End value | Total % average Dmg increase |
|---|---|---|---|---|---|---|
| 10% = | 1000 | *0% | 0 | *2% | 0 | 0% |
| 20% = | 1000 | *0% | 0 | *4% | 0 | 0% |
| 30% = | 1000 | *0% | 0 | *6% | 0 | 0% |
| 40% = | 1000 | *0% | 0 | *8% | 0 | 0% |
| 50% = | 1000 | *0% | 0 | *10% | 0 | 0% |
| 60% = | 1000 | *0% | 0 | *12% | 0 | 0% |
| 70% = | 1000 | *0% | 0 | *14% | 0 | 0% |
| 80% = | 1000 | *0% | 0 | *16% | 0 | 0% |
| 90% = | 1000 | *0% | 0 | *18% | 0 | 0% |
| 100% = | 1000 | *0% | 0 | *20% | 0 | 0% |
Question: What's wrong here? Answer: With the 20% critical damage weapon, because there was no preexisting amp, none of the critical damage in the weapon is actually being utilized.
Base utilizes Amp, which in turn utilizes, critical damage! You cannot have one without the other. The higher your base, the more effective your amp. The more effective your amp, the better your critical damage utilization will be!
Therefore if a character with 1000 base attack, naked, with little to no preexisting amp decides to use the 20% critical damage weapon, his weapon will be limited to using and critting with merely the amp and add attack within a skill.
Now to compare an extended weapon with 40%critdamage versus a 7%amp/28%critdamage weapon.
At 50% rate, you will have an average damage increase of 20% from the 40%critdamage weapon, to compare, an 7%amp/28%critdamage weapon will give you 21% average damage increase at 50% rate...... Only if you have enough total base and AMP, even for averages. Without amp, you can have all the critical rate you want and your overall dps will remain low. Simply because the critical damage isn't actually being used.
At 60% rate, you will have an average damage increase of ((60*140)+(40*100))/100-100=24% average damage increase, to compare, a 7%amp/28%critdamage weapon will give you ((60*128)+(40*100))/100-100=16,8%+7%=23.8% average damage increase. Again, this depends on your base attack or magic attack value and your total AMP.
40%critdamage equipment has the POTENTIAL to be stronger than 7%amp/28%critdamage equipment, but ONLY if there is enough AMP present to utilize all the critical damage properly! For example, a 7%amp/40%critdamage piece would easily out-damage a 40%critdamage piece (because of the additional amp), and it would easily out-damage a 7%amp/28%critdamage piece (because of the additional critical damage).
With this information you should be able to calculate which will suit you better. Important to consider is that amp is a direct amplification of your base attack and/or magic attack. As such, at higher levels (140+), and especially in Battle Modes and/or Aura (which directly increase Base) a 7%amp/28%critdamage weapon or equipment piece will provide greater End attack value then its 40%critdamage counterpart.
So as a rough reference, 40%critdamage equipment is better suited for lower level characters with low base values (since the critical damage would be able to at least boost their skill damage bonuses better), 7%amp/28%critdamage equipment better compliments higher level character stats (since they have the base to better utilize the amp, and thus, the critical damage), and adding critical rate (preferably 7% or higher) to either of these equipment sets is the "Ideal".
With this knowledge it is up to you to search for gear that provides the best combination that raises ALL stats: base, amp, critical damage, and critical rate, and is best suited for your class.
Good luck!