I would like some suggestions on which choice to make on an internally geared hub. I have the choice between a SRAM internal 7-speed and a Shimano Nexus eight-speed internal hub. I have no experience with these type hubs and would like to have some opinions on which is better quality. Thanks for any help.

I have a Nexus 8 hub which I bought second hand. Gear 5 slips. Bike was not heavily ridden prior to my acquisition. YMMV....

The SRAM-7 has an excellent reputation. A fair number of randonneurs use it, and it holds up fairly well under that sort of use. They're also fairly repairable. Shimano hubs do not hold up as well, and aren't as repairable. Some of the parts just aren't available. And Shimano's planned obsolecense means even if the parts *were* available, odds are they're not now. V. depressing.

That said, if you're a "normal" user, odds are you won't wear out a Shimano hub quickly. They do tend to last at least 10k miles if you're not mean to them. For me, that works out to an expected lifetime of about 5 years.

Having had and used both, my reccomendation would be for the Nexus 8.
That said, depending on terrain, and what bike you are going to use it in, a Sturmey Archer 5 speed is a good low cost alternative.
I have a good assortment of gearhubs including 2 Rohloffs, a premium Nexus 8, a Sturmey Archer 5 speed, and now, a Sram i-Motion 9. I just got that one up and running yesterday, and my initial impressions are not really favorable. Here is a thread I posted about it.
https://www.bikeforums.net/bicycle-mechanics/540814-alternative-shifter-mounting-igh-drop-bars.html

My daily commuter bike is equipped with a Sachs/SRAM Spectro 7 IGH with coaster brake. It has been used for the past 7 years of all weather (rain, snow, road salt, -4°F to 100°), daily commuting for approx. 35,000 miles. It still works fine and always has no matter what. It was original equipment on the department store city bike I bought new in Germany for approx $135. The bike still works fine too.

No experience with a Shimano 8 speed but I have a Shimano 7 speed IGH on a cruise bike and it is OK but the shifting gets sticky in below freezing temperatures

I have several IGH bikes and have been riding IGHs for ~30 years.

- Shimano Alfine: smoothest shifting but steps are irregular. I find it annoying on a commuter, no issue in the dirt. Newest version has new guts, 501. Had it working down to -20*F.

- Nexus is good, need to be aware of the model. I'd only consider the 8r25 or 8R35/6. The 8R35 has the Alfine 500 guts, the 8R36 has the newer Alfine guts, the 501 version. Had it working down to -20*F

- SRAM i-Motion 9: it's not as nice shifting as the Alfine, the steps are regular, works well on a commuter, not up to mountain biking. Not so good below freezing, I've switched it to oil bath, should be better next winter

- Rohloff, cost is ~$1600, what's the point?

Here's a couple of good sites for IGHs:

https://hubstripping.wordpress.com/

https://groups.yahoo.com/group/Geared_hub_bikes