Both are really nice hotels, so you can't really go wrong with either.
You can't beat the location of Mirage - it's right in the middle of everything and within easy walking distance of many attractions, shops, restaurants, other casinos, etc. The rooms are fine, and the pool is nice, but doesn't quite compare to the Mandalay pool.
Mandalay Bay is at the end of the strip, and not nearly as convenient as Mirage. There is a tram that connects Mandalay to Luxor and Excalibur, which makes it a little more easily accessible. The pool there is great, and the rooms are better. You can get a strip-view room, but you typically pay extra for it.
We don't typically spend a lot of time in our room, so I personally would be tempted to choose Mirage for the location. If the pool and room are important to you, then I'd choose Mandalay. You can always visit the animals and other things at Mirage, even if you don't stay there.