There is a large difference in kinds of type, which derives from the purpose for which it they were made and, hence, the process by which they were created. Historically, "type" was used in the process of letterpress printing, with ink being applied to the raised surface and from there transferred to paper. Since (until very recently) the whole idea was "kiss impression", with the least possible amount of pressure applied during the process, type could be used over and over again (not indefinitely, but for tens of thousands of impressions). In contrast, applying gilt lettering to leather bindings on a one- or two-off basis required both heating the letterform and applying it with substantial pressure to transfer the gold leaf to the surface...a very different process. For this reason, the image of the letter was traditionally cut out of brass and made with a handle for ease of use.
Moving into the late nineteenth century [bear with me; there's a point to all this history] a lot of people spent a great deal of effort attempting to automate the whole typesetting process. Their attempts ranged from one of Mark Twain's investments (a machine that would replicate a human typesetter by assembling individual pieces of pre-cast type), to other systems that would cast letters or lines on demand. Because of the speed at which these machines operated, it was not possible for them to use the same metal formulation which was traditionally used for 'foundry type' designed to be set by hand, and then re-used. Instead, Monotype machines used a somewhat different formulation which was softer and didn't last as long...but this wasn't a problem because after printing a single job, the type could just be thrown back into the pot and re-melted.
So...that brings us to the present. For hot stamping, which requires a lot of heat and pressure applied to the letterform, your choices in descending order of quality (and expense!) are:
Designed specifically for hot stamping and lettering bindings, brass type is machined from solid pieces of brass alloy. It conducts heat well, doesn't melt, and won't deform under pressure. It is more durable and more uniform in shape than cast type, and deeply cut to give a clear and sharp impression on both hard and soft material. Brass type is usually sold in small fonts (providing just enough letters to make up a few words at a time, which is all you usually need for stamping.) It is available new from bookbinding and hot stamping suppliers, as well as used. Because it is a smaller market than printing, and because fewer pieces (in absolute numbers) were/are made, it is much scarcer than cast type.
Aside from cut brass type and photo-etched metal printing plates, all other type used for stamping is cast from molten metal, either in individual letters or as the whole line to be imprinted. The best cast type, designed specifically for hot stamping, is made from Monel, a hard nickel-copper alloy. It is corrosion resistant, and thus avoids the 'pitting' that sometimes comes with lead type. Monel type, however, is both expensive and hard to find.
Designed to be set by hand for letterpress printing, this was
the the mainstay of the market for a couple of hundred years. It is made of a
lead alloy containing (ideally) 64% lead, 23.88% antimony, and 12.02% tin, with
traces of copper. The largest US type foundry was American Type Founders, a
conglomerate created in 1893 by a merging of all of the major foundries of the
day. ATF, which set the world standard for type, first went bankrupt in 1933,
and then lived on in various incarnations until its final, tragic demise in
1993. For more information (and a great, if sobering, holiday present), see
http://www.daleguild.com/ATF
The Ludlow Typograph is perhaps the most popular type casting machine for hot stampers, as it combines many of the advantages of handset type (simplicity, variety) with the advantages of machine cast type (constant supply of fresh type, easy duplication, single slugs). Ludlow type is softer than foundry type, and thus will last for many fewer impressions...but it then be simply thrown back into the pot and recast anew. Unless you have your own Ludlow machine (certainly possible, and relatively available from used equipment dealers for a few hundred dollars, but bulky, heavy, and probably overkill for occasional users of small bits of type) you will order your Ludlow slugs from one of several vendors who routinely cast Ludlow type for others.
The majority of what you will find on eBay, and virtually all currently cast individual type (with the exception of the Dale Guild type above) is Monotype. This type is cast on a relatively small caster, a piece at a time, and is either made up in batches of a single letter (on a Sorts Caster), or with individual letters already spelling out the text to be printed (on a Composition Caster). Monotype metal was traditionally 78.3% lead, 15.9% antimony, and 5.8% tin. In recent years, however, a number of the Monotype foundries have taken to using a slightly harder alloy in certain cases, with higher percentages of antimony and tin but still not approaching foundry type.
So, the bottom line is that there is a vast difference in type when it comes to hot stamping, which would explain why your results have varied. If you can afford it, get cut brass type. If you're only doing a little bit of work and need unusual fonts, look for foundry type. In a pinch, if you must, you can use Monotype, but it may well deform after only a few impressions.
Following are some words from the horses' mouths on the relative merits of different kinds of type.
Theo Rehak of the Dale Guild on their foundry type:
"Many people ask us if our type can be used for hot-stamping work. Whether it be locked up in a hand-pallet, a Kwik Print, Kingsley, or one of the other machines in use, our Barth-cast type will produce more impressions than any other lead-alloyed type. It is second only to zinc. Many of our hot-stamping customers use our fonts of small-caps, which we font separately, and are very affordable. At present, we have several faces in stock. Limited edition binders make good use of our Hammer Uncial and Goudy fonts as well. "Slugs cast on Linotype, Intertype or Ludlow machines can be used, as can types cast from a Monotype Composition caster, but they will be short lived. The alloys used and the casting pressure determine hardness. Types cast on a Thompson sorts caster produce a harder product, and the user can expect about 100-150 impressions into tough paper or leather. Careful surface imprinting will yield more. Our types are cast on rebuilt ATF Barth foundry-casters, and will yield 6-8 times the impressions at less than twice the price."
Andrew Hoyem of M&H Type on their "foundry Monotype":
"Small sizes, generally through 12 point, are cast on Monotype casters, using metal that is harder than Monotype metal but not as hard as the foundry metal used for Thompson casters. All other font sizes are cast on the Thompson and Giant casters, which use metal containing more tin, antimony, and copper. Softer metal, a lead alloy of Linotype quality, is used for casting leads, slugs, quads, and spaces. Monotype metal is used for rule and border strip material.
Rich Hopkins of Hill & Dale Press, producer of "Monotype University":
"Type of good quality can be made on virtually any typecasting device. That includes Monotype composition casters, Thompsons, Giants, Super Casters, the Bruce, the Barth - and even the hand mold. The Bruce and Barth, as well as the various "foundry" casters used in Europe, all have the potential for casting better type because they have the potential for moving metal under greater pressure. That is, if everything is going well. But that isn't always the case. "There is no question but that ATF type is superior to what we Monotypers cast. They do use better metal and they bought "new" metal, where most of us use whatever comes our way...ATF Barth and Bruce casters cast a more solid piece of type and that also is very important. Speed and automation with the Monotype compromised these matters. But keep in mind, the Mono was intended to make the user his own typefounder and Lanston always strongly advocated "cast, print, dump."
I hope this proves helpful.