Front suspension or full suspension mountain bike
If we assume that both models are at about the same price point, here is what you can expect:


The hardtail will be substantially lighter than a comparably priced full-suspension bike.
The hardtail will likely have a higher level of components and possibly a better front shock because of the increased expense associated with the full suspension frame.
Unless you can lock out the rear suspension, you will have higher pedal efficiency on the hardtail.


Your style of riding may dictate that an full-suspension is appropriate, so the best thing to do would be to describe how you want to ride to the professionals at your local bike shop and listen to their advice.

I have an admitted bias toward hardtails (and even fully rigid bikes). I've been riding a long time (since before mountain bikes existed...), and don't really ride anything seriously aggressive off-road (but I have ridden a lot of Utah Red Rock Desert).  I've tried several full-suspension bikes, but for my type and style of riding I've not been convinced that the added cost to get to a similar weight/component mix was worth it.