The two HI are very close together, both easily accessible by bus or taxi from the airport. They are not in the historical centre of the city, but everything is within easy reach. There's a HEX, but it's just outside Oeiras, on the road to Estoril, in an industrial area.
Both HI give upgrades to plats. Both hotels are inexpensive when there's nothing "on" in Lisbon. They are both bog-standard HI, no nasty surprises.
BTW - the key to a happier taxi trip from the airport is to use the taxi rank in the departures area.
The HI Continental is very close to the Metro (Campo Pequeno) and suburban rail station, surrounded by cafes, and (weirdly) has its own in-house cafe next to the restaurant where the (horrendously expensive) breakfast buffet is located. Better to breakfast in the cafe. There are some excellent reataurants close by. It's a business part of town, spookily quiet on Sundays.
The second HI is between two metro stations (Alameida and Campo Pequno), but quite a hike from each. It has a decent enough restaurant. It is behind the city's technical university in a smart part of town, fringing a pick-up zone for prostitutes. Local resouces
Six of one, half-a-dozen of the other.