If it's on topic, I'm also interested to know how they compare against modern steel.
Toledo steel is a very good steel, comparable to the best contemporary one. It is based mostly on the content of the material and way of hardening.
Damascus is much better, it is based mostly on the way of smithing - folding, beating, folding again,.. repeat a year every day many times a day. With addings during smithing. The precise receipts are not known, and Damascus weapon is better than any contemporary one. There existed close variants - reinventions in other countries, Russian bulat was one of them. The Damascus steel could be extremely sharp and simultaneously, very strong - you could cut a silk scarf by letting it to fall on the blade and you could use the same blade as a belt and you could simply cut a usual sword in two.
As for samurai weapon, it is a widespread mistake, that it had good steel. On the contrary, the steel was bad, in Japanese fencing you should never block the blow, but let it slip along the blade. Though this steel could be sharpen also to the extreme, and the trick with a scarf could be done with it, but it was weak and easily broken or at least dented by any direct blow. The Japanese did the most possible out of what they had, but the resources on the Japan islands are poor.
An interesting professional article on the theme, much more thorough than my answer: http://www.tf.uni-kiel.de/matwis/amat/def_en/articles/vikingsword/blade_patterns_intrinsic.html
The problem is that now all these names are mixed - you can buy a "japanese damascene" for 100 dollars. Not real, of course. http://www.swordsoftheeast.com/damascus_3.aspx.
The secret of toledo swords is revealed now: http://aceros-de-hispania.com/toledo-swords.htm
An interesting personal research with links: http://tf.uni-kiel.de/matwis/amat/def_en/index.html
And one more thing I would like to notice: All these themes are not well-known and closed. They are under research. And probably forever.
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As it is, all three are interesting for being completely different methods of achieving a high quality of steel. Equally interesting is that they are each of high quality in different ways.
As for Tamahagane, the iron that was available in Japan was actually very poor compared to that found in Europe. It had a characteristically low carbon content, and the only way they had to increase the carbon content was to fold it into the steel during forging with a process called pattern welding. This folding did make the steel harder, and thus better able to hold an edge and less likely to bend, but it also meant that it was more brittle and more likely to chip and crack as well.
Damascus steel is something of an oddity when discussing forging technology for two reasons. Firstly, historians don't know if the descriptor refers to the smiths working the steel, where it was sold, or simply a visual similarity to textiles from the Byzantine empire. Secondly, the exact methods originally used to forge the steel in question have been lost to time. Researchers have found the various trace elements within the metal, but they don't know precisely how they were introduced. At its core, however, Damascus steel is basically another type of pattern weld. The problems this introduces are the same that are introduced with modern welding techniques, in that each weld represents a point where two pieces of metal are joined and are thus weaker than a solid piece of the same material would be.
Toledo steel, however, is separated from the other two in that it is a true alloy. Toledo steel is created by permanently mixing the iron and the other chemical additives through smelting. The difference is visibly evident by the observing the consistent appearance of Toledo steel versus the layered patterns of both Tamahagane and Damascus steel. Of course, like the other types of steel, Toledo had its drawbacks. Because of the extremely tight tolerances of the heat used during the smelting, forging, and tempering processes, the steel took an incredibly long time to create. This lead to the widespread use of daggers and shortswords, as they required less material and thus less time to create than a full-sized sword.
As for determining which of them was the best, that is completely subjective, depending on the desired characteristics, much like deciding which is better between a wrench and a hammer. A wrench is good for turning bolts, but a hammer is good for driving nails. Similarly, it can't really be said which method of producing steel is better without defining the criteria. Tamahagane could be honed to an incredibly sharp edge, but was too brittle to be used for blocking. This was fine, as most combat with katanas and similar weapons was against combatants in leather or lacquered bamboo armor. I'm not sure of the hardness characteristics of Damascus steel or the type of armor that it would have been used against, but due to the similarities it has with tamahagane, I imagine it faced similar challenges as well. Toledo steel, being produced in western Europe, would have often been used against more heavily armored opponents or against shields. For this reason, it would have been less important that the steel be able to hold a perfect edge than the tendency not to break when impacting something it couldn't cut straight through.
So, to answer the original question of a comparison between the three kinds of steel, I doubt that you would be able to find anything that addressed it without doing so in the context of making blades, as steel that was used for other purposes was typically of a different formulation. And, to answer the second question, contemporary formulas have been invented which surpass all three in just about any category you could think of. After all, there have been thousands of years of technological advances since the invention of these methods, depending on which you are referring to.