About 100,000 words in the English-to-Japanese section, 187,000 in the Japanese-to-English (including 90,000 keywords and 97,000 phrases, sayings, and example sentences). Here's the description in Japanese.
In general, I'd say that with Edict and Eijiro, most people won't have much use for Kenkyusha. It is well supplied with example sentences and usage information, but so is Eijiro--and Eijiro is 10-15 times larger. Edict doesn't have much of that sort of help, but simpler words, as are likely to be omitted in Eijiro, really don't need it. You can take a look at the screenshots below, comparing typical entries in Kenkyusha to their counterparts in Eijiro, and see if you think it's worthwhile for you. I offer Kenkyusha not because I think it's essential but simply because there's some demand for it--it's one of the best known English-Japanese dictionaries, it's typical of the E-J dictionaries you'd find in standalone electronic dictionaries like the Canon Wordtank or Casio Ex-Word, and it's reasonably priced (I'm not sure exactly which dictionary is in which electronic dictionary these days, but Kenkyusha is in quite a few of them). Other commercial E-J dictionaries are 2-3 times the price of Kenkyusha without offering any significant advantage.
For about 25-30,000 yen, you can get the Big Green Bible, the full size version of Kenkyusha, with more than twice as many entries. I'd have to order that, so if you're interested, please ask on the Order/Enquiry page and I'll get back to your with the current price and an estimate of how long it will take. It's a great dictionary, but that's a lot of money.
Here are the screenshots. The usual caveat about resolution and appearance applies--the dictionary will look a lot better on your VGA PDA than these shots will look on your monitor (see below; click each image for a full VGA version).
For more information on how to use the EBPocket software and the PDA itself, see the general documentation.
Note that I've sized the images above to appear about the same physical size as the Axim X50V's screen (depending on your monitor, of course); however the actual Axim screen squeezes a full 480x640 pixels into that space, so it's much sharper and easier to read (more pixels in the same size=higher resolution). You can click each image to see the actual 480x640 pixels you'd get on the screen of an Axim or other VGA PDA, although because the image will then be much larger than on the Axim screen it still won't look quite as sharp as the real thing. And of course you can change the text size to be larger or smaller, too, which will also affect legibility.