I would encourage you to use whatever style door you like. At 6' long I would not recommend hinged doors that open sideways as they'll swing out pretty far.
Many people prefer flip down doors. I don't particuarly like them but that's my personal preference only. I have no objective argument against them.
One thing to consider is that your cages will likely require a center support of some sort, especially since you'll be stacking them. Double flip down doors may look nicer with this support that double sliding doors. Not enough to make me choose them, but it's something to consider.
But to answer your question, double sliding doors are very easy to build. The rough opening needs to be fairly close to square, but that's really the only trick.
There are some design issues to consider to insure sliding doors work properly. I can go into those once you decide which design you'd like to use.
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I am going to be making two stackable wood cages that measure 6ft by 2.5ft by 2.5ft. I am not sure what I would like to do with the front of the cage. I am by no means a skilled wood worker so whatever I do will have to be halfway simple. Would it be difficule to make sliding glass doors? I am open for any and all thoughts. Thanks