There are advantages and disadvantages, in my opinion the pros outweigh the cons.
Advantages:
Lighter weight than NiMH pack of similar voltage, increases power to weight ratio
Maintains higher average voltage, combined with increased capacities you can get by with fewer packs
Does not require extensive maintenance to maintain performance, periodic balancing only - no discharge / equalize cycles and associated equipment
Minimal self discharge - charge on Monday and race the following Sunday without having to re-peak
Disadvantages:
Current chassis' designed around Nickel cells, though this seems to affect on-road disproportionately
Lighter weight - can cause balance issues which may require addition of ballast thus negating weight savings
Requires different charge algorithm, not all chargers compatible
Yes, LiPo packs cost a little more. However if it's possible to get two to three runs from one pack with consistent performance, they really aren't any more expensive than your average matched NiMH packs.
I believe the current commonly held belief that LiPos are inherently less safe than NiMH cells is due in large part to misinformation and lack of knowledge. If charged using an appropriate charger with the correct settings and used in a manner that does not exceed the packs recommended discharge capabilities they are very safe. They're not going to explode in a horrific fireball if you look at them the wrong way.