I’d say both seem underpriced but a lot depends on where you live, finishes selected and what is existing In the basement.

Estimating anything other than floor finishes using a cost/ square foot metric is a sure fire way to get into trouble--particularly with remodeling projects. Cost is driven by a variety of factors including project scope and the expected quality level. For calibration purposes, you'll be well served to look at cost data for your area in Remodeling Magazine's annual Cost vs. Value Report

https://www.remodeling.hw.net/cost-vs-value/2020/

It's one thing to finish a basement that was built for being finished in the future. It's another to carve a kitchen and bath out of nothing, which sounds like what you're doing. Sounds completely reasonable to me.

Does that just cover installation and building materials or all the other items such as cabinets, fixtures, flooring, countertops -- all the things you see?

We finished our basement a couple years ago - maybe 1400 sq ft. We had some changes so I'm not sure the final number, but for installation/building materials it was probably $60K (maybe less), but then I bought all of the other things myself - flooring, cabinets, fixtures, tile, etc. etc. In addition, I wanted foam xps insulation, rockwool insulation and some other improvements and so I paid the increase of those. And that all added up - particularly since I had the ejector pump replaced, sump pump/battery system replaced, fireplace, dishwasher, microwave, etc. etc..... I have never added it up!

https://youtu.be/omZvd2Vd3PA

Have frequented wondered what build-out costs run. Guess I should be feeling pretty good. I finished our basement shown in the link DIY about 12-15 years ago. No bathroom. About 650 sq ft. My investment was around $15,000 plus my time.

The basic basement around here without a bathroom starting price is approx. $25 per SF with bathroom add additional 8-12k depends what goes into it.

Some basement companies who work on volume advertise basic basements for $10 per SF.

That said that was before Corona hit now with lumber going for almost $6-7 per stud the prices are slightly higher. $100-150 per SF you can build a complete "cookie-cutter home".

Both are too low.

Basements used to just be drop ceilings and berber carpet. But now, they are where a lot of "luxury" amenities are added...bars, home theaters, exercise rooms, etc. It would be impossible to get an accurate per sqft estimate without detailed plans and a lengthy conversation about expectations. In my market, basement remodels are often in the six figures. The $25/sqft price you're reading about? Probably drop ceilings and berber carpet.