I hope your decision wasnt based on how either car starts, but since you asked i'm going try my best to answer based on my experience

but first of all, i would have test driven both cars first before making any decisions; Make sure you take into consideration all aspects of buying a car like functionality (how it starts), cargo space needed, power, etc... and most importantly price.
Either way, both cars are excellent you wont go wrong with any of them.

Now regarding your question about how the car starts: I own an 06 prius, and to start the car you just have to press a button, the car runs on electric only for a few seconds, then the engine starts up ( it's programmed); depending on the outside temperature; if it's a hot day, the engine shuts off right away after about 30 seconds and the car returns back to electric mode only; so you can drive around in total silence and depending on how much charge there is; you can actually accelerate up to around 50+km/hr without using the ICE at all (excellent for very congested traffic where you have to stop very often, saves a lot of gas). But accelerating hard requires the help of the ICE and then when you're up to speed, it drives to the next RED stop light on EV only.I do not own an HCHII but fortunately, i have read that it does drive on EV mode too when you're up to speed. Having test driven both, It's definately true that they are both very silent compared to just regular cars when you both start them: gone is that sound where the starter cranks the crankshaft before the ICE finally kicks in

Good choice & good luck with your car!