Well, I have some real world experience in that for you. My place, just outside Ottawa, Canada has had geothermal since before I moved in > 15 years ago. It can hit 100F here in the summer - sure, it's not Texas, Florida or Arizona, but can get quite hot - and humid. Combined with skylights and quite a few south and west facing windows, it has the potential to get quite toasty in here. My geothermal (which is a terrible misnomer - more accurately they are referred to as a ground source heat pump), has zero issues keeping it cool (70F) in the summer. They are actually quite a bit more efficient cooling than they are heating. My system is open loop, meaning I pull water from my well and it discharges into a pond maybe 100'' from the house.
In the winter, again, it can get quite cold, down to -35 or so at times. Again, it has no problem keeping it warm enough in the winter either (again ~70F). The key is, they need to be sized appropriately.
would natural gas (for heating at least) be cheaper? Yes. I do not have access to natural gas. Some form of electric (including geothermal), oil or propane are my options. The geothermal is definitely cheaper than the other options - especially how crazy propane has become in the last 18 months or so. There is a high upfront cost though. The units alone cost ~$20k at this point I'm guessing. That doesn't include putting in vertical or horizontal loops if you're going closed loop. I believe that some jurisdictions would not allow an open loop system like mine.
So to answer your question, yes, they're capable of keeping you comfortable. You just have to figure out if the high upfront cost is worth it to you in the long run.