All pickups, regardless of type, will translate some of the resonant characteristics of the guitar, its woods and the metals used in its components. Perhaps what XevKai objects to is the overall flat response of actives, no matter what guitar they're placed in. It's not an exact comparison, but guitarists have generally preferred the tone of passive pickups over actives for the same reason they prefer guitar speakers and cabinets over high-fidelity flat-response PA speakers and cabs. They prefer the specific frequency profile that those speakers provide, with the best ones emphasizing a very flattering blend of midrange, a clear but not glassy high-end response, and an emphasis on thump rather than mud in the bass.
Active pickups provide a much flatter response curve than their passive counterparts, meaning all frequency ranges are represented more equally. They then transform this signal with batteries to provide a significantly higher output. In the days when actives first entered the market, this extra output drove medium-to-high-gain amps into very desireable levels of gain, making an amp sound 'hotter' than it would with passive pickups. However, even from the beginning, many guitarists started to notice that, for all their additional gain (which was very popular among the metal crowd), they sacrificed somewhat in tone. Too much for many to make the switch.
Active pickups developed a reputation early on for sounding "sterile" because they didn't filter out certain frequencies from a guitar's signal the way passives do. Glassy, even irritatingly strident, higher frequencies were part of the gain/tone trade-off, as were mids that were flat, lacked character, and most importantly, didn't "sing" for lead playing. Bass response was actually not such a big objection when actives first came out because the overall increase in bass response didn't create as many problems in the pre-Recto days when amps didn't have a huge built-in bass response themselves. Sustain was actually pretty good, given that early active pickups used fairly weak magnets to generate signal. Today, some actives have combined active circuitry with stronger magnets and, while power has increased, sustain has nearly disappeared in these units.
Due to their flatter tone response, active pickups generally require some rather precise EQ'ing to achieve what most guitarists would find a desireable tone, especially for music outside of only the very heaviest of metal. In that respect, they can be likened to an uncarved slab of marble. Beautiful tone can be coaxed from them, but often you must first sculpt out the tone response curve you want with a good graphic EQ. You must also take into account the type of amp you'll be playing through and its general tone response, as well as the speaker cab you'll be using, and adjust accordingly. You may find that they require more significant cuts and boosts with the sliders than you are used to using when EQ'ing passive pickups.
For those with the patience and/or curiosity to do the extra tweaking necessary, active pickups can yield both good tone and powerful output. However, as I have mentioned previously, I personally would rather not have to do it that way. Instead, I prefer to choose a passive pickup whose tone I already like and which fits the wood of the guitar I'll be using it in. If I need more raw power to the signal, I'd rather be able to switch in or out a good clean boost to that already good tone. Any EQ'ing necessary after that is usually minimal and subtle. A passive pickup run through a modern boutique clean boost provides a much stronger signal than even the hottest active pickups do on their own, so power is not an issue.
With today's high-gain amps such as exemplified by the Mesa Rectifiers, a really hot signal from the guitar isn't all that necessary anymore. This is a large part of the reason why high-quality overdrives have started to take some of the market share away from clean boosts and active pickups. Today's boutique overdrives usually provide much higher clean boost than their predecessors, but they also add in a certain degree of distortion and harmonic content that give a guitar/boutique overdrive/high-gain amp rig much greater harmonic bloom and density of signal than is possible with either active pickups or clean boosts, no matter how powerful they are.
Ultimately, it's a subjective matter of preference. There is no answering the question of which is best. Truly good useable tones can be achieved either way, you just have to know what you're doing. The most demanding tone freaks are usually the most intense tweakers, so that shouldn't scare anybody off. Just find the sound you like best and work with it to get it to sound exactly the way your ears like it and you'll be happy, whichever pickups you choose.
