Gil (usmcdoc14) put a lot of time and effort into testing various upgrade options that is worth taking your time to read: https://www.jkowners.com/forum/showthread.php?t=85577
The first thing, and I can verify this from personal experimentation, upgrading just the bulbs themselves with more expensive H13 bulbs is not going to make a significant difference. The reason is that the OEM reflector itself has a dead spot in the middle of the light pattern.
However, it does seem from Doc's tests that replacing the H13 bulbs with HID capsules not only generates more light but a much better light distribution pattern, and without the unfocused glare usually associated with HID drop-ins. At least this was true with the Rebel Offroad HID upgrade, and is probably true for other HID drop-ins as I'm pretty sure that Rebel didn't have the capsules custom-made. The good news is you can order HID drop-ins for under $100 off Amazon.com and return them for full refund if they turn out to not produce the quality of light you want. Remember when ordering HID drop-in kits you need Lo/Hi beam with H13 connectors and an anti-flicker harness option.
I've never seen H13 LED drop-ins in use and it's extremely hard for me to believe that they can produce any better brightness or quality of light versus a good H13 halogen bulb. There just isn't enough surface area to dissipate the heat needed, or to even mount LED elements within the focal zone necessary for a proper pattern of light. Also, unlike HID's which use ballasts to boost the rather weak voltage the OEM bus presents at the headlights, the LED's would need additional circuitry to regulate voltage to an optimum level, and again, there just isn't enough room to incorporate the additional circuitry using components that can withstand long-term use at high power draw.
The option that's worked well for me is replacing the OEM headlight lamps with quality H4 E-Code lamps such as from Bosch, Cibie or Hella and good bulbs from Osram or Hella, in combination with a full replacement wiring harness to run the headlights via relays off the battery, with the relays triggered by the OEM headlight wiring. Again, you have to incorporate an anti-flicker harness (or connect capacitors and diodes across the relay trigger terminals) to filter-out CAN BUS signals. You can buy the H4 lamps and bulbs for $80-$130 and buy the components needed to do a plug-and-play wiring harness with no splicing or soldering for around $70.
In my unscientific comparison, my Bosch H4 e-Code lamps with Hella H4 100/80W bulbs produces similar reach and pattern to $800 J.W.Speaker LED's for 1/4 the price.