PS (aka. “Type 1”) fonts: PostScript outlines. Separate files for outlines and kerning (on Windows, but not on Mac). Rigged to encode only a max of 256 characters at a time, in predetermined encodings (echoing Bill Gates: “Who will ever need more than 256 characters!?”) Characters and features such as extended ligatures, small caps, and old style numbering live in separate fonts — just today, I got a font where I had to type a “K” in another font to see an “fi” ligature.
TTF fonts: TrueType outlines. Huge character sets — full Unicode 2.0 set supported. No feature-enabled re-coding, though — if a font has small caps or oldstyle numbering, it'll be in non-standard positions, and you will have to select and insert the characters manually.
OTF: Outline format: either of the above, and I couldn't care less which one. Who can tell by looking if a font uses quad or bezier curves? Mega ultra size character sets (Unicode 3.0 — is there a 4.0 forthcoming?). Features can be enabled and disabled per user request, enabling access to language sensitive characters (S cedilla vs. S comma-below, o kreska rather than o grave), more ligatures than a sane person could ask for (anything is allowed, viz. the custom “Zapfino” logogram if you type its name, and the amazing Ed Interlock), context aware kerning, and typographical niceties such as hand drawn superiors and inferiors and real small caps. Amazing possibilities.
So, it sounds you should convert everything you own and then some more to OTF. Or, does it?
If you convert a font to OTF, it will not have all the niceties I summed up. Special ligatures have to be drawn — or, if they exist in another font file, copied to the base font file. Small caps ditto. And then you have to add the mini OTF programs that actually allow these automatic replacements to take place — it doesn't happen by itself.
I'm also not totally 100% sure of the kerning conversion that takes place. Are all existing kerning pairs correctly converted? All you have to do is type “VAT”, and you'll see if it does. Oh — and all extra OTF types of kerning (class kerning, context aware stuff) should also be added manually.
So there are no real benefits of converting your fonts, and only (possibly) drawbacks. Your computer (or specifically, FontExplorer) doesn't mind handling all different font types. Sure, OTF has lots more possibilities, but you'll have to add them yourself, and that amounts to completely overhauling each and every font.
Unless anyone else can convince me, I'm sticking to my old (t)rusty PS fonts, unless an official Pro version comes out — now these are worth upgrading to!