My Peugeot PX-10 has this rather beaten decal showing it's made from Columbus SLX tubes. Paint is in pretty good shape. I'm hesitating about one step in restoration:

Should I replace it with a duplicate decal, or leave the "authentic" barely-recognizable brand?

For anyone voting to replace, any tips on removing the old one without damaging the paint?

Replace. The new ones look great and go on easy.

Good question. I'm faced with the same decision on one of my bikes.

So how do you remove old, beat-up stickers and/or decals from a frame which still has decent paint?

Leave it alone. It will only be original once. It's just a tubing decal.

If you absolutely must remove the decal - if it actually is a decal - i.e., a sticker - you can try using a blow dryer to heat up the adhesive backing, which will re-activate the glue and make it tacky again while it is warm. Carefully lift and edge with a finger nail. I'm very good with an X-Acto and I can use the flat of the blade to start the lift, but I don't recommend that for anyone who doesn't use one every day. Don't try to remove it all at once: heat a little, lift a little, repeat, repeat, repeat. You can also try Bestine (rubber cement thinner, available at artist supply stores) as a solvent to remove remnants of the adhesive, which can otherwise be quite tedious to remove. Two cautions: (1) Be careful with the blow dryer; it can heat up the tube very fast and you can easily burn yourself quite badly. You might also damage the tube. (2) Most solvents - especially Bestine! - are highly flammable, so don't use it around open flames or even a running blow dryer. Solvents can also be absorbed through the skin and ultimately cause damage to the good old central nervous system, so wear gloves.

Or you could leave the original decal alone.

I agree with Robbie. Especially when the rest of the bike is in good condition and the tubing label looks like it was just exhumed it from a peat bog, it's time to replace.

PS - Old water slide decals sometimes come off with a little WD40.

If it is a water side decal, you can also go to a hobby shop and purchase decal softening solutions. They're designed to soften decals so they'll conform to irregular surfaces but you can use them for softening and removing decals.

The decals are so fragile that paint polishing compound may also remove them . At the same time it will remove the ground in dirt from the paint.

I'm in the "remove and replace" crowd.
Like Pichio said, it's just a tubing decal.

I'm debating the same thing in regards to an oblique 'Reynolds 531 frame tubes' decal. I've almost decided to save what is left. In fact, I have already clear coated it, so the rest is not going to flake. Yours (like mine) looks like a water slide type. And if it is, a strong wind will eventually blow it off! If it is crinkly, the decal softener mentioned above is a good idea. Then you can either spray a clear coat on the entire tube after masking off the other tubes off to prevent overspray — or alternatively spray a puddle of clear into a small container and dip an artist's brush to paint the remaining decal out to within just a mm beyond its boarders. Should stay there indefinitely. And it will be original. And it will very likely not fade in UV if it has not already done so, something that may not be true of a replica depending on who made it and materials used.

If it's not covered by a clear coat, adhesive tape is often sufficient. If it's stubborn, squirt of WD-40 helps.