I think we should be careful to break the English and American traditions apart. In the United States, the substantive difference between law and equity was the remedy available. At law, you could only get money; in equity, you could get injunctions. There were special pleading rules for each kind of suit, so the distinction was actually significant. In the federal courts and in the courts of 47 states, this distinction between law and equity was abolished. Courts are now competent to grant both kinds of remedies.
You want $100,000 in damages from me? Go to federal district court. You want an injunction against me? Go to federal district court. You're in the same court and you fill out exactly the same forms; you follow exactly the same procedures and file exactly the same documents. Indeed, sometimes law and equity are mixed up in the same suits. If Apple sues Samsung over a patent and requests $10 billion in damages, it probably also requests an injunction barring Samsung's use of the patent at the same time; and at the very beginning of the suit, Apple probably tries to get an injunction against Samsung that prevents them from selling products that violate the patent. Same court, same procedures, all flowing together.
This distinction between law and equity shouldn't be confused with the use of equitable principles today. The judge can invoke equity as he pleases, and much court procedure today actually originated from the equity courts, so indeed, judges are constantly invoking equity. When you said a plaintiff with unclean hands won't have much luck with equity, you mean the judge isn't going to be tempted to gloss in his favor in making a decision--the judge will just refuse to invoke equitable principles. This has no legal significance (other than potentially being bad for our plaintiff). Thus there is no substantive separation between law and equity, you just have one court that's competent to grant whatever remedy it believes appropriate.