Just to add a bit more. We will take a Sony VTC5 as the example, though the numbers will be basicly the same with a VTC4 (just not as much capacity). So a fully charged VTC5 puts out ~4.2v (4.15~4.25v). If the battery has no sag and the mod has 100% efficiency then you could pull a max of ~126w from the battery when it had a fresh full charge. At the very end of its usable range is 3.2v. Again with no sag and 100% efficiency you could pull a max of ~96w from the battery.
Pretty good but this will never happen in real life since all batteries have voltage sag under high amp draw and no mod is 100% efficient. Mod max input amps are 30 for this example.
Sony VTC5 with 30a draw has a sag of ~0.5v at full charge and the mod has a 95% efficiency. At full charge you are looking at ~105.5w and at the very end of its range (~2500mAh) you are looking at ~81w (the sag is actually only about 0.35v at the end of its capacity and 30amp draw).
How about a LG 18650HE2? I'll give it at 25a and 30a (beyond rated, but so you can directly compare to the VTC5 above).
LG HE2 with a 25a draw has a sag of ~0.6v at full charge and mod has a 95% efficincy. At full charge you are looking at ~85.5w and at the very end of its range (~2200mAh, it drops through the floor past this) you are looking at ~65w (sag is about 0.45v at the end of its capacity and 25a draw).
LG HE2 witha 30a draw has a sag of ~0.8v at full charge and mod has 95% efficincy. At full charge you are looking at ~97w and at the very end of its range (~2200mAh, it drops through the floor past this) you are looking at ~78.4w (sag is about 0.5v at the end of its capacity and 30a draw).
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The LG HE2 is a nice battery, but as you can see by the above it is below the VTC5. In real use it is even worse though since the VTC5 has a fairly smooth drop over its capacity, very tight consistant sag, and the low numbers of its range above are at about 2500mAh. The LG HE2 has a steaper drop off (much steaper at the begining and end), experiences more sag at lower amp draw, and the low numbers of its range above were taken at 2200mAh. Why did I stop them at 2500mAh and 2200mAh? Because past that they are going into damage the cell over discharge.
If I had posted results at about the middle of their range (say 1200mAh) and the Sony VTC5 at 2400mAh for its final numbers the differences would be even bigger.
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So this is comparing two actual good batteries (well, the VTC is a great battery). Crap batteries will have way more sag at higher amp draw, have far less of their capacity actually usable without over discharging the battery, run much hotter, and have much higher risk of something nasty happening.
Even at low max input amp limits, the higher draw rated batteries are a better choice. They will have less sag, run at a lower temp, have better battery life (less sag means less amps required to met a given wattage requirement), and normally have a longer useful lifespan before you have to buy a replacement.
(BTW if anyone is wondering, the Samsung INR18650-25R is a touch better than the LG HE2 in sag and usable capacity before)