It's not really important, but the math nerd in me is cringing. It can't be worse; it's mathematically impossible for it to be worse on average. If the two systems are set to average out the same kills per item then badges will always have a lower or equal standard deviation.
Let's say the standard item is a 10% drop rate. To have an equivalent system you could do something like require 10 badges which have a 100% drop rate, or you could do 5 badges with a 50% drop rate. In all three situations the average kills per item is 10, but the badge situations have a much narrower distribution for the amount of kills required. No one using the badge system has a chance to get an item on their very first kill, unless 1 badge = 1 item (which is still no worse than before). It's also far less likely that after 100 kills someone won't have at least 1 item with badges than with only item drops.
For badges to be more variable than the existing system you'd have to do something where you get more than 1 item per badge, such as a badge giving two items, which MMORPG developers almost certainly wouldn't do.
Hm, let me rephrase: it's not technically 'worse', but it may possibly feel like it.
In your example the drop rate is pretty good, so it would work well.
Let's use another example. The drop rate would be 5%, so you'd need 20 badges to get the reward. Now let's say you have 3 people who want the reward, and 1 guy would always have priority for the badges that drop.
The 3rd guy, who needs to do 60 runs before he gets the reward, may get discouraged more easily than if there was a random chance- you might get 2 items in a row like that, if you get lucky. The chance for that to happen might be what makes him come time after time.