Natural is always better. But it also take HUGE amounts of time
Sync'ing decreases time to heat check, but I think you can expect a 5-15% decrease in conception.
Time'd AI will decrease time dramatically, but also will decrease conception the most. Depending on who ya talk to, and luck, expect conception of 40-70% (more likely 40-50%).
So, if you have lots of time to heat check (21 days minimum for 8-12 hours a day), then I would definately go natural. If not, do the figuring and weigh the pro's and con's of price, conception, and time.