Not difference in ESR - difference in Vf, and not only the lab-measured Vf, but actual in-circuit Vf, which is a function of the LED die temperature, in a really bad way - higher temperature lowers the Vf, increasing the current of the already hottest LED, until it is destroyed.
Hence, avoid paralleling LEDs. This being said, it's still normal to do that, but you need to really know what you are doing. So if you end up doing that, make sure you thermally couple them, i.e., the thermal connection to the heatsink must be not only good, but also consistent between the LEDs, and the heatsink should be thick enough (or use a heatspreader) so that there isn't temperature differential between the LEDs. In addition, derate the current a bit from the maximum rating. Also, the LEDs should be of the same production batch / grouping.
Putting them in series lets you use maximum ratings because now you can regulate the LED current in all LEDs, guaranteed, within the accuracy of your current regulator circuit of choice, easily within a few %; completely regardless of Vf. You can even use different colors in series.
Series connection can mean cost savings if the LEDs are the most expensive part, you can better utilize them with less derating.
The downside, or upside, depending on the power source, is the requirement of higher voltage. Thus, the power source and your preferred current regulation scheme are important parts of the choice and should be discussed before you can choose whether and how much to parallel.
If the power source, for example, is 12V, one way to do it is to use a boost current regulator, but in order not decrease the boost efficiency too much, the voltage cannot go arbitrarily high, so you end up somewhere 30-40V max. If you have more LEDs than that, then you can create multiple strings, but each need their own regulators. Easy to design by copy-pasting, and scales well, but consider the cost. For example, if a $2 boost drives ten $1 LEDs, that's likely acceptable, but if a $3 boost drives five $0.20 LEDs, it's likely a no-go.