Audio Processor: The AC-1 uses the C-Media Oxygen HD CMI8788 APU, while the Prelude uses the Creative X-Fi... if you play 3D games, the X-Fi is superior for sound processing in a 3D sound-field.
DAC: The Prelude and the AC-1 both use audiophile quality
AKM AK4396 DACs (digital-analogue converters) which are infinitely better than those used in your Logitech speakers, so using the soundcard to do the DA conversion is a much better choice over relying on the relatively low-end speakers to do the job...
Op-amp: The Prelude uses National LM4562 Op-amps on the analogue outputs, which are very high quality, you can change these out to something like the TI Burr-Brown OPA627 or OPA637 using SOIC-DIP8 converters ("Brown Dog") for a quality which is better (or different, depending on your taste) to the LM4562 (involves soldering the SMD chips to the 8 pin converters)
The AC-1 uses Analog Devices ADA4850 Op-amps on the analogue outputs. These aren't as well known in audiophile circles, and I haven't heard them myself so I can't vouch for them, although AD make some really nice Op-amps.
In terms of stock sound quality, I think they will sound quite similar as they both use the same DAC and assuming the AD op-amp is high quality (most probably is) then the analogue output is going to be very good on both soundcards, certainly better than relying on the Logitech DAC.
The advantage of the Prelude is that it uses the X-Fi audio processor, so it can handle much more 3D positioned sound in games, and is therefore more accurate in a 3D soundfield. It also uses DIP8 sockets for the op-amps, so you can replace them with other op-amps to improve/tweak the sound to your preference without desoldering the stock chips (just pull them out of the socket), and replace them with alternative DIP8 chips, or solder some SOIC chips to DIP8 adapters, and plug them in the sockets...
Judging your rig spec, I'd say go with the Prelude, better for gaming, opportunity to improve the sound with minimal effort