Even though you get relatively flat voltage across the life of a rechargable, you still have a high voltage spike with freshly charged batteries.
For example, freshly charged NiMH may be 1.4-1.45V (1.2V nominal), fresh Li-Ion are 4.1-4.2V (3.7V nominal). You still must deal with the initial higher cell voltage. So you either set your resistor to properly drive your LED with the nominal voltage, and accept higher current for the first bit of battery life (possibly overheating and/or damaging your LED), or you pick a resistor that safely drives the LED with the high initial voltage, and suffer lower current later. For alkalines vs NiMHs, you pretty much have to deal with the same voltage range.
In addition, Vf changing due to temperature and life of the LED can also change the set current.
A linear regulator (if that's what you're referring to) satisfies all conditions. You don't have to worry about the initial higher voltage of rechargables, nor do you have to be concerned with Vf changing. When the input voltage is less than about 2V above the Vf of the LED, they can have great efficiencies, as well as providing flat output. They do best when the input voltage is just above the Vf of the LED, there efficiencies can be better than 90%.
Buck regulators go a step further and get you a little more battery life (by drawing less current when the battery voltage is higher) at the expense of higher cost and complexity. However, some buck regulators don't work well when the input voltage is just above the Vf of the LED, since some don't allow the switch to hit 100% duty cycle (just a technical detail there). Mainstream buck circuits are in the high 80's for efficiency, advanced in the high 90s.
So it depends on what you're after. Personally, I like my lights driven by a regulator, even when being driven by rechargables. Both of my Lux V lights will fall out of regulation when even NiMH cells are over 80% discharged, so when they start to dim, the batteries are dead, and it's a sign to change batteries.