In the given example there's not much difference. But there can be a great deal of difference in other constructions involving the same idea. Consider:
I only eat fish when I'm sick.
I eat fish only when I'm sick.
I eat only fish when I'm sick.
I submit that the first sentence is a bit ambiguous, and could be clarified in the direction of the second or third. Two and three mean entirely different things.
NOTE: In spoken English it is relatively easy to make the first sentence unambiguous by use of a vocal stress on the part you wish to indicate belongs with only.
I only eat fish when I'm sick. (I eat only fish when I'm sick.)
I only eat fish when I'm sick. (I eat fish only when I'm sick.)
I only eat fish when I'm sick. (I eat fish only when I'm sick.)
Certainly you can do the same thing in writing or typing via underlining or italicization, but sentence structure is perhaps a simpler way to draw the distinction, requiring no additional adjustments.