I'll separate this answer into the sections that you've outlined.
The wilder has one major advantage in both 3.5 and Pathfinder. The wilder can manifest much more powerful powers than Psions and other full caster psionic characters. While other characters have access to Overchannel, Wild Surge has much more raw power. When you don't get hit with enervation, you spend a lot less PP for a lot more power as a Wilder than you do with other character types.
In 3.5, the Wilder's other class features are largely inconsequential. Surging Euphoria and Elude Attack are pretty nice, but they aren't huge benefits for a full caster. Volatile Mind is also nice, but also effects allies and doesn't effect nonpsionic effects, which sort of neuters it.
In Pathfinder, the Wilder has better class features, but they compare decently with the extra class features that the Psion gets, so there's no effective gain.
The wilder has two big disadvantages when compared to the Psion. This first is in power selection. The Wilder gets 11 powers at 20th level, where the Psion gets 36. This basically means that where the Psion is comparable to a Sorcerer in versatility, the Wilder is even more limited. With 11 powers, the Wilder has to be incredibly careful with their power selection, and still will only end up with a few different kinds of solutions that their powers can solve. In addition, Wilders don't have native access to psionic discipline powers, which are typically very valuable and powerful.
The other big disadvantage is Enervation. While the chance for Enervation is lower in Pathfinder than in 3.5, there's no real difference in how bad Enervation is. Losing a turn (or being staggered, or taking other pretty bad penalties) and (effectively) one use of your highest level powers is a huge penalty. On a particularly unlucky day, you might end up being able to manifest significantly fewer powers than usual, and lose quite a few turns. This is a huge problem, because in order to use the ability that the Wilder gives up a ton of versatility for, they need to risk taking a significant penalty.
The Wilder doesn't have any real unique benefits. While gaining exact copies of the Wilder's class features (in either 3.5 or PF) might be difficult, none of them are really that great. While the benefit of Wild Surge is strictly better than the benefit of Overchannel, the penalty of Overchannel is much less painful than the penalty of Enervation. In addition, the flavour of Overchannel is basically identical to the flavour of Wild Surge.
Some of the PF Surge Bond types give interesting benefits, but none of them are particularly powerful.
There are a few ways to mitigate the weaknesses of the Wilder class, but they are costly and they don't really help that much.
In both 3.5 and Pathfinder, Wilders can take the Enervation Endurance and Expanded Knowledge feats. Enervation Endurance makes enervation only take half your level in power points, and Expanded Knowledge lets you gain more powers, including powers from psionic disciplines.
In 3.5, Wilders can take Postpone Enervation, which delays the effect of Enervation, but that's really not a great option. 3.5 Wilders can also take the Educated Wilder alternate class feature from a web supplement that exchanges Volatile Mind for four Expanded Knowledge feats, which is a nice trade.