Shooting with the flash in Manual mode vs. eTTL is analogous to shooting in Manual vs. Av mode on the camera. There's no real functional difference: everything you can do in the automatic mode you can do in the manual mode. The basic trade-off is one of precise control and consistency over speed.
eTTL, as a term, is used to mean three different things that can be loosely lumped under the heading of "extra fancy flash features"
. In order of what's most commonly meant to least commonly:
1) Automatically setting the flash power based on through-the-lens (TTL) metering. The flash sends out a flash burst of a predetermined brightness, the camera meters the "preflash" burst and then sets the flash power to what it deems the appropriate level for exposure, and then takes the picture with the automatically set power burst. You typically don't see the flash bursts individually, it happens so fast.
The basic drawbacks of using eTTL to set the power are that it's based on metering, so it can shift between frames, it can be thrown off the way all metering can be thrown off, and you have less control. You do have FEC (flash exposure compensation), that's similar to regular exposure compensation, but it's not the same as explicitly setting the flash to be at 1/8 or 1/32 power.
2) The infrared/light-based proprietary signaling system that Canon uses to wirelessly communicate between flashes. This is the one that requires the master unit on the hotshoe, but will give you the auto-power-based-on-metering.
I think I already covered the drawbacks to this, but essentially range, reliability, and line-of-sight are the main weaknesses of any infrared-light-based signaling system. For use outdoors, blocked visibility, or larger range, you want radio triggers.
3) The additional features that you can get with the flash on the hotshoe or using the Canon light-based system: high-speed sync, stroboscopic mode, remote power-level setting.
Of all these extra features, the two most off-camera lighting geeks lust for are the high-speed sync (i.e., being able to use a shutter speed higher than your max. sync speed. This is a physical limitation of the camera body--you can look it up in the specs. For most camera bodies, it's around 1/200s or 1/250s), and remote commanding. Because when your flash is 100' away and hung up over a basketball court, it's kind of a pain to get to it to adjust the power level.
So, yeah, eTTL has some good features, but the main drawback is that it's very expensive to do wirelessly (and wasn't even possible wirelessly until a couple of years ago when Radiopopper hit the scene) and most eTTL-capable sync cords just aren't long enough for proper off-camera work--they're usually designed for attaching the flash to a bracket, so you may have to
hack your own cable.