The trade-off, stated plainly. A testamentary trust is cheaper and simpler to set up than a living trust, because it is a few extra paragraphs in a document most people need anyway, with no separate instrument, no funding exercise and no retitling. What it costs is everything a living trust is usually bought for. The property has to pass through probate to reach it, so the estate carries the delay and the administration expense. The will, and therefore the trust's terms, become part of a public court file when the will is proved. And because it does not exist during life, it offers nothing at all if the testator becomes incapacitated; the documents that answer that question are a durable power of attorney, a healthcare directive, or a funded living trust.
The typical use, and why it is a good one. Without a trust, a minor cannot hold an inheritance directly, and property left outright to a minor generally ends in a court-supervised arrangement over the money until the child reaches the age of majority, at which point they receive it all. A testamentary trust replaces both halves of that: it names a trustee the testator chose rather than one a court picked, and it releases the money at an age the testator chose, which can be twenty-five or thirty or in stages. The same structure works for an adult beneficiary who should not receive a lump sum, whether because of a creditor problem, a disability, or a history the testator does not have to explain in the document.
The line between a testamentary trust and a pour-over will is statutory, not a matter of description. A pour-over will devises property to the trustee of a trust that already exists, or that the will itself brings into being under a separate written instrument. Both states whose enactments are cited on this site say expressly what that property is not. Montana's version of the Uniform Testamentary Additions to Trusts Act provides that, unless the will says otherwise, property devised to such a trust "is not held under a testamentary trust of the testator but it becomes a part of the trust to which it is devised and must be administered and disposed of in accordance with the provisions of the governing instrument setting forth the terms of the trust." California's enactment says the same thing in near-identical words. So the poured-over property runs on the living trust's terms, not on the will's, and the will's own residual clause is not what governs it. A testamentary trust, by contrast, has no governing instrument other than the will.
A tax difference that is easy to miss and occasionally matters. Internal Revenue Code section 644(a) provides that "the taxable year of any trust shall be the calendar year", with narrow exceptions at (b) for tax-exempt and charitable trusts. An estate is under no such requirement: the Internal Revenue Service's own instructions for Form 1041 state that "the estate's first tax year may be any period of 12 months or less that ends on the last day of a month", and that choosing any month other than December adopts a fiscal year. That flexibility can be used to shift a spike of post-death income into a second year. Section 645 lets the executor and the trustee of a qualified revocable trust jointly elect to have that trust treated and taxed as part of the estate for a defined period, which extends the estate's advantages to it. A testamentary trust is not a qualified revocable trust, since it was never revocable and never existed during the decedent's life, so the 645 election is not available to it and it is on the calendar year from the start.
Whether the court keeps watching afterwards is a question for the state, and one state's answer is worth reading. People often assume a trust created by a will stays under the probate judge's eye indefinitely. California's Probate Code says otherwise, and says it narrowly: continuing court jurisdiction over a testamentary trust applies only where the will was executed before 1 July 1977 and not incorporated by reference into a later will, or where the will itself provides that the trust is subject to the superior court's continuing jurisdiction. Under a modern California will, in other words, the supervision exists only if the drafter asked for it. That is one state's rule and not a national one, and no general answer could be established here — so treat ongoing supervision and periodic accountings to the probate court as a question about the state where the will would be probated, not as a feature of the instrument.