For making things simpler from marketing perspective manufacturers upgrade not only groupset with the next level, but many other components too. So overall in this price range you should not only be getting more gears, but lower weight, more reliable and higher quality components, better brakes etc. It could be even the difference between bottom bracket standards and chainsets which could make your life a little bit easier when it comes to service effort / service range.
Regarding speeds - more gears just give you smaller gaps between them, you can see it yourself that both 8 speed and 11 speed cassettes could provide you the same range of 11-28 or 11-32 (hardest gear size - easiest gear size), so going flat out or going uphill should make no difference. except the weight savings.
So answering your questions, you need to count in more factors to be able to make a choice. What's your expectations on a bike? How long do you want to keep it? In my opinion in this price range you get good value for money each time you pay a little bit extra. At the same time I'm sure it's possible to find Tiagra if not 105 bikes for the same price if you look for less mainstream brands, buy online or wait with the purchase to make it during autumn/winter season.
UPD: also would like to loop in the factor of resale value. I believe for lower spec road bikes it's usually quite low, while I can see people sell Ultegra bikes for something like 75% of the new price, when it comes to Claris I can see ads with only 50% of the price of the new. So at the end buying slightly more expensive groupset could save you some cash, worth checking out your local market of used bikes to make a decision.