The lower your stats are, the more happiness matters. If you are training at all, it matters. If you are going to be 100% fighting, it doesn't matter at all. . . . but if all you do is fight, it is kinda hard to win with low battle stats.
The more you focus on training, not just happy jumps but any training, the more it matters. You can turn on and off your happiness depending on what you are doing. For example, if you focus only on training for a full month, go for as much happiness as you can get. If you will be mostly fighting, say for the Halloween event, you might skip the PI rental.