i can't answer if the audio processor is any 'better' in this case. for me, that is personal preference. while computer-based audio processing is overall more expensive when looking at the costs(pc was probably in the range of $1,000, soundcard was about $180, software will be $200) it is much more of a hassle to set up, but can be configured in any direction you want it to be. a audio processor-- as i'm sure you've already looked at the cost-- is about the same as your overall pc cost, normally a little less. but there is very little setup-- just plug your cables into it, configure some settings-- in some cases, they are automatic, and you're done. normally, they cover every aspect that you really ever need to adjust to get a good soundstage, and as a bonus, they are not reliant on the pc working to make your sound system work.
but even after all that, i personally prefer the adjustments that the computer-based processing gives me--even though it is more expensive and time consuming, simply because i can do whatever i want with it, whenever i want to do it--which is half the fun of a carpc for me. in the same respect, i don't really need a carpc either
as for the line driver, i would say that is something to consider after installing the carpc. many are happy with the volume of a setup like that, but just as many aren't-- again, it's personal preference as to which side of the fence you fall on..