I'd opt for an i7. Hyperthreading can help but clock speed improves performance and xeons aren't as fast as the i7. The cost savings aren't all that huge when considering the budget. The gains are more noticeable if the i7 6700k is overclocked.
Here's a rough comparison, it's between the i7 6700 and 6700k stock. The xeon e3 1240 v5 (skylake) is only 100mhz slower so this is a best case for a xeon vs the i7 6700k. The skylake xeon that compares evenly with a 6700 is the e3 1275 v5 and it costs $30 more than the 6700 while the 1245v5 is around $30 less than the 6700.
http://www.anandtech.com/bench/product/1543?vs=1554
At stock the 6700k processed 604 fps in handbrake while the 6700/1275v5/1240v5 (all about the same performance) scored...