Whoops. Voted wrong. I meant to vote "Yes" instead of "No", but got confused by the first post and was thinking "Should bonuses against different types of units be used?" to which I do think "No" is the correct answer.
Having played both Civ3 and Civ4, I found the bonuses against certain types of units to be one of the major items I disliked in Civ4. It works well in a game like Age of Empires II, or even III. There, if you are attacking with Knights and Two-Handed Swordsmen, and they have Pikemen and Crossbowmen to defend with, part of the challenge is to get your Knights to their Crossbowmen and your Swordsmen to their Pikemen. You might come out on top, or your enemy might - it depends on how both of you play. In Civ4, if you attack with the Knights, you'll have to face their Pikeman with the Knights, and if you attack with the Swordsman, you'll have to face their Crossbowman. It's a lose-lose situation. And it's not more realistic. The defender is not always successful in getting the ideal troops to defend their camp or gates.
Civ3 isn't perfect, either - if the enemy has all Pikemen and you send in Knights, you should do worse than if you send in Medieval Infantry, and this isn't the case in Civ3. But at least you don't have the discouraging Civ4 system where no matter what you do on the offensive, the defender always gets an ideal defending unit if they have combined arms.
So while the idea behind the bonuses versus different types of units wasn't bad in principle, it didn't work well in practice. There needs to be some way for a Knight to attack a Pikeman/Crossbow stack and actually reach the Crossbow. Maybe a trait "Can avoid ideal defender - 30%", that could be upgraded with the promotion system. If the Knight succeeded, it would face the strongest defender before any bonuses against certain types of units were factored in. It'd throw a monkey wrench in the current combined-arms defence system, but I think it would be an improvement overall.
The alternative is to factor in all the different units in a tile and have some conglomerate of that determine the odds. But that gets away from the one unit vs. one unit system, and could lead to all sorts of consequences (think Giant Stack of Doom Uberstategy). Not that it can't work (a la Total War), but it may be a larger departure from the classic Civ that's been around since 1990 than would be good for the series.