I have ridden both bikes. KLX 300 stock and very modified, and DRZ 400 mostly stock. For a casual trail rider, both bikes are really quite good - better than an XR4, IMO.
FWIW, the kickstart only DRZ is a super easy starter 99% of the time - cheaper and lighter than the electric start. Comparing stock to stock, the DRZ has a substantial power advantage over the KLX 300. The DRZ really doesn't feel as heavy as it is except under hard braking or very tight conditons.
A big bore (331cc) KLX300 with suspension mods is a really fun bike on the trail, with a very wide range of usable power. Excellent handling and light for a 4 stroke. But it's true, the modified KLX can be very hard to start if you drop it, and the stock KLX 300 is just a little too soft in the power department. The KLX pegs are also pretty low - sometimes this is annoying.
Unless you have the time and $$ to do the KLX mods, the DRZ is better, IMO.
At 240 pounds, your brother will want stiffer springs for either bike, even if he is slow.
After dialing in a DRZ or KLX, a good rider will have no trouble keeping up with an average rider on a CRF or YZF. For the average trail rider, the DRZ or KLX are excellent bikes, but the KLX needs a little more attention to get the most out of it.