The primary attibute of tantalum is they can make them down to 2 wvdc breakdown voltage allowing a lot of capacitance in a small package. An alum oxide you won't find much below 10 wvdc, so for low voltage applications like battery operated portable devices they will be larger.
Tantalums have a bit higher Rs then alum oxide at low frequency but the Rs stays constant to a higher frequency compared to alum oxide electrolytics.
If it fits, you can most of the time substitute an alum oxide electrolytic. Some rare cases, the Rs of tantalum is used for a stability pole on output of a voltage regulator, but it is a rare case that it makes a difference.
Tantalum is a rare commodity so they are more expensive then aluminum electrolytics.