Dry yeast vs. liquid yeast won't in itself make any difference, the differences will be mostly due to the strain of yeast.
However, you may be pitching different amounts of each. Dry yeast sachets have nearly twice as many yeast cells as liquid yeast packages when made, and dry yeasts are a bit more shelf stable than liquid yeasts. A properly rehydrated package of fresh dry yeast will give you twice as much yeast as a fresh WYeast or White Labs package. This gets worse if the packages are a few months old, or haven't been stored in the fridge during transport. This is why it's advised to use a starter on liquid yeasts. Underpitching will result in more esters and yeast character generally.
Given a proper pitching rate, the strain of yeast will be the determining factor on how much esters and different off-tastes are produced at different temperatures. US-05 is reportedly peachy tasting when fermented cold (e.g. 64F), although I'm not sure if that's from ester production. English yeasts (e.g. S-04, WLP002, WY1968 etc) will be cleaner at around 64F, but generally produce a lot more esters if fermented above about 68F, while US-05 is pretty clean at that temperature. WLP001 will be as well. Other yeast strains may behave completely differently.