I don't find D20 overly rules-heavy -- I said it before, look at RoleMaster or Hârnmaster or even The Dark Eye and THEN say again that D20 was rules-heavy. However, it could still use some simplification in certain aspects - with Grapple rules being the worst I can think of.
D6 pool games like Shadowrun or West End Star Wars are quite nice, but tend to be rather die-heavy. Having to roll like 15 or even 30 d6 in Shadowrun (at least in 2nd and 3rd) is no rare occasion, especially for advanced characters. And my old SW smuggler character also rolled >10d6 on his primary skills.
Besides, most d6-pool based systems seem to be used for Scifi/modern settings; I don't know why that is, but maybe there is a reason.
(GURPS is a different story, because you don't have dice pools there.)
Also, just looking at the dice and the way they are used can tell you a lot about the system and what kind of game it supports. For example, a system using a single d20 yields a linear distribution of results - it is as likely to roll a 1 or a 10 or a 20. A system using 2d6 (and adding the numbers) has a Gauss distribution; it is a lot more likely to get an average result than an extreme one - the chance of rolling 6-8 is almost 50%! (44,44% to be precise) -- similarly for any system that rolls a number of dice and adds the numbers.
In short, those multiple-dice systems make checks more predictable. "Average" tasks are solved more reliably, but on the other hand, extreme tasks are a lot more difficult and less likely to succeed.
Of course this is just a small aspect of a system, but together with other points, it can give you an idea whether it supports a heroic style, and _this_ would be my primary concern when looking for a system for Conan.
On another note, while I generally like class-less, level-less systems (like Shadowrun), it just needs to fit well with the game world. Class-based systems have one huge advantage, and that is niche protection. Each class has its unique abilities that can't be taken from it. Class-less systems tend to make everything available to everyone, so in the end, those characters are often very similar.
As for levels or not, that's basically a question of power curve. Level-less systems have a smoother and less steep advancements, whereas level-based systems often have power surges, especially early in the game, and (often) a generally steep advancement.
That being said, I think that a level- and class-based system is ideal for a heroic sword-and-sorcery game like, well, Conan.