If I were to reccomend one over the other it would definitely be photoelectric for a few reasons.
1. Photoelectric does not degrade over time. I change mine every 10 years so it's not really a problem for me, however if you are like my parents and have been meaning to change theirs for the last three years (the smoke detectors and you were already overdue by 15 years your smoke detector won't work at all.
2. Ionizing has way more false alarms and is often is set off by water vapor or even stupid things like toasters. If you want to be waving a towel in front of your kitchen or bathroom smoke alarm then get ionizing. This can lead to people unplugging them and then forgetting to plug them back in.
3. Ionizing is cheaper, so you are more likely to select a cheap Chinese version. Many ionizing are high quality and Kidde is a reputable brand. Kind of a stupid point but it is what it is.
4. As for response times, both detectors work. Yes you may get a slight headstart on an ionizing in the event that the house is burning very fast, however I think both types of fires will be present anyway. If you have a massive fire thats caused by newspapers or something it's going to light something that smokes on fire eventually whether it is a couch or the paint on the walls or something. Vice versa if there's insulation slowly burning in my walls it will eventually turn into something big. In summery I don't think type of fire would really concern me too much.
Anyway, after saying all of this, I think I will install a ionizing smoke alarm in the near future just to be on the safe side.