The latest version of the Zoom H4n the H4N Pro is good and is much heavier than the DR05 as it has XLR connectors that make it easier to connect the better microphones. This latest version also has good pre-amps i.e less background noise from is electronics. I have one that is slated for evaluation soon. I gather that it still guzzles batteries and start up time gets longer the bigger memory card you use.
There is a significant difference in weight, cost and bulk, but it is more flexible and you will be able to use it for most portable recording needs more easily.
I havn't used any hand held Zoom recorders much yet, but compared to the bigger Tascams such as my DR100 MkIII the battery consumption is a downside - the DR100 has an internal rechargeable battery, internal back up AAs and a takes a bolt on battery pack that has to be manually switched over. However we are now entering the same arms race as we see on the photography and binocular forums.....and as several threads point out for complete security of power you need to move up to the big luggable recorders.
Battery performance is usually in the specification section of the instruction manuals as is info on the best memory cards etc., you will learn that battery performance has minimal corrrelation to the number of batteries the recorder uses. I have an old Yamaha unit that runs for ever on a single AA cell!
There are no perfect audio recorders, just those that work for you best.
I also have a Zoom H5 lined up, that being a later generation than the H4 is rumoured to have slightly better battery consumption, but has interchangeable microphone modules including a short shotgun, but I record other things as well as birds, so I need flexibility for the portables as my most powerful recorders are totally unsuitable for field use.
For investing for use over a long period the Zoom H4N Pro is a good choice, for simple use and excellent value for money the DR05 is good, I could come up with other choices, they will all have their downsides as the less expensive end of the market is mainly designed for musicians and reporters.
So - of the two, I would personally go for the Zoom, but I will make full use of it (as you may after a while), but the Tascam DR05 has a lot of followers too, decisions like this can drive you mad you know....
At the end of the day - follow your dreams and learn with whatever you've got and as Mark says you can do wonders in post processing.