Dedicated AC Power Line vs. Power Conditioner?

Depends on how good your current line is.
IF your current line is not used for any other devices.. And is not on the leg your refrigerator is on... Then most likely not much improvement.
If your current line has two dimmers for lights on it, and is used for other things, and taht 'leg' has the refrigerator on it, then yeah, a separate line will be great.

Also IF the wires to your outlet are broken by several other outlets.. And the new lines will be direct. the too could mean it will get better.
(though you can bypass those intermediary outlets to imporve your one used for audio instead. Just rune the wires together through them, wit pigtails to the duplex in each. or even just make certain none of the intermediary duplex outlets have the power running through the break off tab on each duplex (the vast majority DO use one screw of the side on the duplex outlet for in, across the tab, then the other screw to continue the powerline. which sucks.)

So, depending on your arrangement it could be helpful, or a waste of money.

If you have two 15 or 20 amp lines added, be certain they are on the same LEG of the incoming 120v 120v 0v
So no dangerous 240V potential can be between your equipment.

The resulting loss of noise from isolating your audio system from other lines is well worth the relatively minor expense if you have a fairly resolving system.

The "versus" part of your system sets a bit of a false dichotomy IMHO. It's not a matter of either or. Improvements in power delivery are cummulative.

If you heard the improvements the Tice brought to your system, you will probably hear what a seperatepower line does. Finally, if you hear what the seperate power line does, you might be amazed at what the latest generation of power conditioners can do.

I agree with everyone so far. It was a great help in my system to add two lines to keep the components separate.

Who could recommend someone who knows what they are doing to install dedicated power lines without charging through the roof?

It shouldn't be that expensive, assuming there's no structural rebuilding needed. Just to run wires from panel to existing boxes cost me about $300, 150 per line. It old be less if you can find a certified electrician doing side (after hours) jobs for cash.