In the wake of the economic collapse, Broward and Palm Beach counties are veering apart in their strategies for dealing with their budget crunches. Broward plans to cut the Sheriff’s Office budget and leave property taxes at current rates. Palm Beach County residents may face tax hikes as large as 15 percent. Rates would still be lower than Broward and Miami-Dade counties, officials assert. Robert Weissert, spokesman for the watchdog group Florida Tax Watch, said government should find a way to do more with less. Palm Beach County’s property tax rate will be voted on in September, and would go from about $3.78 per $1,000 of taxable value to $4.34.