The difference on the bottom end is negligible compared to the gain on the top end. I doubt you would notice the difference between 3 to 4.5 and the difference from 9 to 14 will be a benefit. Even if you don’t use 14 power all the time, you can still use it at less power if you want.
That's how I see it. However, you also have to consider weight and balance a factor as well. You get a little more top heavy with a 4.5-14x. I've used both and love the 4.5-14x42 and 4.5-14x44 rifle scopes, but eventually trade them out for the smaller and lighter 3-9x40's. Off the bench, the bigger scopes shine. Out in the elk timber I prefer the smaller scope.