Short answer. The one the other was attached to. Article 467 of the Civil Code says that as between two incorporated things, the principal is that to which the other has been united as an ornament, or for its use or perfection — not necessarily the larger or the costlier of the two.
What the law says
The principal thing, as between two things incorporated, is deemed to be that to which the other has been united as an ornament, or for its use or perfection.
Civil Code, Article 467 — Which Thing Is Principal. Read the full provision →
The test is purpose, not size or price
The article states it in one line: The principal thing, as between two things incorporated, is deemed to be that to which the other has been united as an ornament, or for its use or perfection. Three relationships are named, and all three point the same way — you ask which object was serving the other. A thing added to decorate, to enable, or to complete something else is the accessory; the thing decorated, enabled or completed is the principal. Bulk and cost do not decide it. A modest item can be the principal if the expensive one was added to serve it, which is why the enquiry starts with why the joining happened.
Why the label carries real money
This matters because of what follows from it. Where two movables belonging to different owners are joined so that they form a single thing and cannot be separated without injury, the law does not split the object — the owner of the principal takes the whole, and must indemnify the owner of the accessory for its value. Good faith and bad faith then adjust the figures: a person who joined another's property knowing it was not his stands to lose more, and may answer in damages besides. Where the two can in fact be separated without damaging either, separation is usually the sensible answer and the question of principal never has to be decided.
How it looks in ordinary disputes
A replacement engine fitted into a vehicle is united for the vehicle's use, so the vehicle is the principal. A frame built around a painting is an ornament, so the painting is the principal even if the frame cost more. A part machined and installed into a piece of equipment perfects that equipment. Paint, tiles and fittings applied to a structure serve the structure. Run the same question in each case: strip away the assumptions about who paid more, and ask which of the two things existed for the sake of the other. That is the enquiry the article actually poses.
Where this rule does not apply
It governs movables joined together, and only where the owners are different people who did not agree in advance on what would happen. If there is a contract — a repair order, a supply agreement, a lease with an improvements clause — that contract governs and this default rule is irrelevant. It also does not reach buildings, plantings and works on land, where land is treated as the principal under its own set of rules; nor mixtures of grain, liquids or money, which are dealt with separately; nor the case where someone works another's material into a new object. Before invoking any of it, take photographs, keep receipts showing what each part cost, and try to establish who joined the things and whether they knew the other item was not theirs.