Lisbon, Portugal versus Madeira

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The two destinations (Madeira is in Portugal) are not comparable at all. I'd check the climate temperature and rain numbers for March first. But Madeira has local transportation issues (unless you rent a car) the the mainland doesn't have as much. Madeira is perhaps a shadow of the upper-class resort it was in pre-war (?) times, but still has a lot of beauty and charm. Note that it has virtually no sand beaches. Big hotels have salt-water pools on cliffs above the ocean, instead. The famous Llevadas offer superb light (perhaps not "rugged") hiking, with a lot of variety, but we didn't have time for that on our short stay. The few mountain peaks can be fogged-in a lot.

2 different trips
All depends what you want to do.

Madeira has many beautiful hikes but not much to do otherwise, after you have hit the major sights.

We were there at end of March, weather was nice for us 19-20 degrees Celsius, perfect for hiking.
You do need to rent a car. Our base was Funchal both trips and you can easily do daytrips all over the island from there.

Lisbon plus Cascais\Sintra can easily keep you busy for a week, you could do it without a car rental. Lots to see, but not many hiking opportunities. End of March will be cooler than Madeira for sure.

Keep in mind that you might have to spend one night in Lisbon at both ends of your week if you go to Madeira. Weather/Winds are unpredictable on the island, our flight was cancelled on our last trip, we just made it for our return flight home after lots of stress finding another flight. If you can fly to Madeira all on one ticket from your home, do that, it will be simpler if you encouter delays.
PM me if you would like hikes suggestions.

We definitely plan to go to Madeira again.

We have never been to the southern European portion of the world...

This covers a lot of potential destinations that would probably be great in March (less so in the full heat of summer, IMHO). Plenty to choose from in addition to the two named locations.

I've been to Madeira twice, for a total of about 10 days, but not at all recently. I found it gorgeous and was able to see quite a lot of the island by using the local buses. I'm sure having a car would be more efficient for trips outside Funchal.

The levada walks often have fabulous scenery with views of terraced hillsides and/or the ocean. I think you'llfind at least one walking guidebook available locally. The levadas are irrigation ditches, so a walk along a levada will be basically flat. There might be some uphill walking required between the nearest bus stop and the levada. There must also be some non-levada walks with significant elevation change.

Although it's a small island, Madeira has quite varied terrain. There are bananas growing at sea level and fir trees higher up. I believe the top of the island is above the tree line. Because of the elevation at the center of the island, some rain is to be expected, but temperatures are generally mild year round.

Lisbon is a very attractive and interesting city. It's totally worthy of being your destination. It's quite hilly, so simple city sightseeing can give you quite a workout if you eschew public transit.

If you decide to do Lisbon instead of Madeira, there are a number of hiking opportunities in Sintra. There are forest and beach hikes, plus lovely dune walks at Guincho beach. Sintra is easily reached by train from Lisbon. Then, you can easily and cheaply get to the Sintra hills via Uber or Bolt.