Each has strengths and weaknesses.
Pellet stoves are primarily for heat but most do look nice. I have a Quadrafire Castile insert. It heated my 3 story house from March to Thanksgiving using 37 bags and I live in Philly. Daily maintenance simply scrape out firepot with putty knife provided and refill pellets in hopper. Weekly, pull lever to empty firepot into provided ashpan. Annually, thorough cleaning of baffles and venting. Pellets currently about $350/ ton, which should last about 1-2 months for most people. Needs minimal clearances to combustibles. Flexible venting. Awesome heaters. Run off T'stat or remote T'stat. Takes about 20 min. to heat up. Can run unattended as a zone or supplemental heater. About $3-5K installed.
LP is quick and convenient. Can operate off simple low voltage switch, T'stat, or remote (basic or T'stat). Can turn flame down. Realistic logs and embers. Optional convection fan. Flexible direct venting and close clearances increase possible locations and applications. Caution with LP leaks and cost of LP. Listed as a vented room heater so use for zone or supplemental heat.
Check out [url=http://www.fireplaces.com]Fireplaces: Fireplaces.com for gas fireplaces, electric fireplaces, wood fireplaces and stoves![/url] to compare. I strongly recommend an NFI Certified Tech to install either.
Keep the fire in the fireplace.