Chrome plating adding weight is no myth. See below.
Pretty simple... polishing only really works well on aluminum, but requires upkeep. Magnesium, for example, will oxidize much more quickly, and you will constantly need to touch up the finish unless you have it powdercoated with clear. Aluminum only needs touch up every once in awhile, but will require that you maintain it to maintain the shine.
Powder and/or ceramic coatings are an alternative. You can get a ceramic finish on your intake manifolds that closely resembles polished, doesn't require upkeep or as much upkeep, and has the fringe benefit of coating the piece with a thermal barrier, keeping heat out of the intake (for example). The piece is grounded and positively charged powder is sprayed onto it, resulting in very uniform coverage. On something like the 13B-REW upper extension manifold, where the surface is slightly bumpy as cast, it will smooth in (but not perfectly) the surface and the result is a "like-polished" part.
Powder and ceramic coatings are available in a range of colors (powder is available in a wider range) and you can mix and match. You can do a "chrome" base coat and then do a candy blue over it, for example, for a custom finish.
It's expensive if you are not doing a number of pieces at one time, since they like to use their booths for one color at a time, and switching over for one piece is cost prohibitive. If you can get in on someone else's color (ask 'em what they currently have set up) it's cheaper. For example, if they're doing a big lot of parts in black, you can piggyback for cheaper rather than forcing them to switch over to red for your part only. The parts are baked after coating, and the material "sets" into a very durable, (usually) high-gloss finish.
Plating also grounds the part and uses a positive charge to cause material to adhere to the surface of the part, but in this case, the materials are metallic in nature. Chroming a part results in a deep shine, makes the part very easy to maintain (Windex window cleaner and a paper towel are all it takes to shine it up again, as opposed to rubbing with your favorite brand of aluminum polish). It does add weight to the part, which can actually be somewhat significant, if that's one of those things you care about. Chrome plating a wheel can easily add a pound or two to the weight of the wheel, depending on how much material was added.
The main difference between all of the above are the cost, the method of maintenance, and the look of the finish.
Polished aluminum costs, because of the detail work involved. It could easily cost you as much as $200 (I know from personal experience) to polish just the upper intake extension manifold for the FD, unless you have a bulk job, or can get your parts sent in through a vendor who has a good relationship with the polishing shop.
Keeping the shine requires elbow work every so often, and can be a pain. The finish is brighter, in my opinion, than either of the other two options.
Powder or ceramic coating will create a nearly smooth finish, and in the case of "cermachrome" (or whatever the shop calls their chrome-like finish) will create a very bright finish, almost as bright as polished aluminum. The price can be high or reasonable, depending on how many pieces you have done, and again, on whether you can get in on someone else's batch, or go through a local vendor.
The finish is easy to upkeep, and requires little maintenance, but it will not be as bright as polished aluminum. To get (and keep) that look, you could have the aluminum polished, and then powder coated with clear. Spraying polished parts with clearcoat enamel doesn't work well, because the material has very little to stick to. In an engine environment, it can also yellow, and with repeated heat cycling, may crack. I wouldn't recommend it as an option.
The problem with powder coating is that it is difficult to do this on a part which has a mechanical component (like a ball joint in a suspension arm) that might require replacing after the piece is baked. It is also possible that some parts will not retain their original dimensions after being sandblasted to prep for the application of the powder coat, also. This is usually only a concern with thin wall material, like a part fabricated from thin wall mild steel tubing, for example.
And finally, there's chrome plating. Chrome is very easy to maintain. If done well, it has a very nice finish, but where polished aluminum will have a bright, almost white tinge to it, chrome (in my opinion) has a deeper, bluer tinge. Depends on what you want. The cost may depend on the size of the batch, but should be pretty standard depending on the size of the part to be plated. Prep should be roughly the same as powder coat, as far as the sandblasting of the surface in preparation for bonding of the metal, so you have the same things to watch out for.
NOTE:
Chrome plating a wheel can easily add a pound or two to the weight of the wheel, depending on how much material was added.