Salt is less expensive, but I prefer Roundup because I don't want the sodium introduced into my soil. For $1 worth of Roundup, I know that the stump will die and that the Roundup which leeches into the soil will be harmless. (I buy Roundup in the huge containers and the price per ounce is very economical that way.)
For many stumps in an area in which I'm not concerned about the sodium, I would go with the salt. And, of course, inexpensive sodium nitrate provides a double benefit: It helps perform a somewhat quick kill on the stump (still not as fast as Roundup), and it provides the first step in a very, very good method of burning a stump and its root structure.
Interesting question for which I don't have an immediate answer: Does the use of Roundup or sodium impede the absorbtion and distribution of nitrates throughout the stump and its root system? In other words, is the distribution of the nitrate optimized by a still living stump and root system?
Gideon
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M.Paul wrote I also drill vertical holes into the stump, but instead of roundup I fill them with table salt.