I haven't tried the NiMH in the eTrex, but I have used them in several Garmin four cell models (12, II, III, etc), and they are just a waste of money in my opinion. They just don't have the longevity of the alkalines, you end up having to carry several sets just to get you though one work day, whereas a set of Duracells could last up to a couple of days depending on use. When I go out on a job I'll pay a visit to Costco and buy Duracells or Kirkland brand in the bulk packs.
I am sure that the Li AA's would work well but they are too expensive in my opinion. This may be the best option if you are storing the GPS for long periods of time between use or it is strictly for emergencies and being stored in a survival kit, the Li batteries have a very long shelf life.