Malta or Portugal/Spain 10 nights in January

I'd do a deep dive into weather stats. There may very well be a great chance of sunny days, but then I can also imagine gloom. The cities of Andalucia could be nice in winter, but I'd have misgivings about the Algarve.
Plus for Malta is you can see every inch of all three islands in 10 days, though Comiso is more lovely in spring when wildflowers are in bloom.

We were in Malta in January, just over a year ago. Alas, it seems a lifetime ago. We were there for 14 days and didn’t see everything. The weather was pleasant for touring, but it was not beach weather. I would not stay in a beach-focused town: it would definitely be off season. If you rent a place, be sure it has heat. Restaurants were sometimes chilly (no heat) and a warm room felt good at night.

I would try to spend some time on Gozo. We were there 4 nights. We did a lot of walking here. The tourist board puts together walk itineraries, with commentary which were very nice. They can be combined, if you want something longer.

There are amazing prehistoric sites in Malta. Don’t miss them! Go to the museum in Valletta to get a good overview of Malta’s history, the prehistoric period was especially well done and you can see most of the treasured finds.

For guidebooks we used Lonely Planets and Bradt. We used the bus system for transport. It is easy to use and goes everywhere. On Gozo the bus only ran once an hour, so be organized, walk, or hire a taxi (at rates higher than the rates clearly posted for tourists, so we walked).

We really enjoyed Malta and we thought January was a nice time to visit.

I have visited the Algarve and southern Spain/Andalusia in January and I have experienced both reasonable weather and also very cold, wet miserable weather, Spain being worse than Portugal. Average weather stats aren’t much use these days, as we rarely get average weather compared to historical data, with global warning influences.

I have been to Malta in the summer. All are places, along with Cyprus, where Northern Europeans go to escape the miserable weather further north. There is enough to keep you occupied in all locations for 10 days. From my experience, the food and wine is more interesting in Spain and Portugal.

If you hire a car, ensure that you mention that you are taking it into Portugal as you may have to pay a small premium. Due to Covid and Portugal’s infection rate, the road borders have been closed. Who knows what the situation will be later in the year? Vaccination is way behind some countries.

Buses run regularly from Seville to Tavira and Faro in the Algarve and take about 3 hours.

Both Spain and Portugal are better from March onwards. In all your options, January is the coldest and wettest month of the year. I head to the Canary Islands in January for a better chance of sunshine and less rain.

I think the first commenter mixed up Comiso with Malta; Comiso is a town in Sicily, not Malta. Anyhow, I have been to Malta, and 10 days is not too much. I only spent 4 super packed days there (due to combined Sicily trip) and could have easily spent more without seeing it all. I would consider splitting your time a bit to stay at least a few days in Gozo, which is accessible via a ferry. Even though Malta is super small and compact, it still takes a bit of time to hit the small villages which are dispersed around the island. The weather can be cool and windy at the time you're suggesting, and probably less sunny than usual. But, on the upside, it will be warmer than elsewhere in Europe because it's so far south.

Do some research on Malta using the Bradt Travel guide or Lonely Planet. The bus service in Malta was great when I went in 2015. No need for a rental car anywhere. Gozo is more rural, so maybe consider one there.

I imagine the reference to Comiso is actually Comino which is a tiny island in Malta but not probably a priority to visit in January. With 10 days available I'd split my time with 2 or 3 days staying on Gozo. Although it is straightforward to travel between Malta "main island" and Gozo, it can be time consuming by bus/ferry, especially if starting out from south of Valletta; so I wouldn't recommend Gozo as a day-trip when you have the time available to actually stop for a night or three.

I've never been to the Algarve in Winter, but really I think at that time of year I would focus more on cities and major sightseeing towns. Personally, with 10 days I'd just do Andalucia, perhaps splitting your time between Seville for the West and Granada for the East. However, if you want to go to Portugal there are (or, at least were, pre-virus), regular coach services (Damas and Alsa I think), between Sevilla and Lagos (and perhaps other stops in Portugal). I don't recall how long it takes, but driving your own car is about 3 hours to Lagos or 2 hours to Faro - so longer than that.

Southern Spain, (particularly away from the seaside and even more particularly higher up, e.g. Granada), can be very cold at night. Make sure your accommodation has heating! It wouldn't be a surprise if it rains on some days, but you'll be unlucky to get 10 days of poor weather. Some days it should be sunny & bright and even shirt-sleeve warm during the middle of the day. (though the locals will stay wrapped up as if they were in the Antarctic).

Stay in one place for 10 nights, no way.

Yes I meant Comino, thanks. In May, I'd strongly urge going over (though I found the boat trip terrifying frankly--too small a boat with questionable life jackets). In January, there would be no reason to include that day trip if it was even possible. Gozo was indeed wonderful for walks--I believe we traversed the entire island on foot, used buses as well. I'd split it roughly 4-6 with Malta.
Malta is nearly effortless, so it really just comes down to what kind of trip you want!

Based on observation from the ferry, nobody was going to Comino in January.

Cyprus is usually much milder and drier than Malta as it’s much further south. It has some good old amphitheatres, ancient churches, castles, the Tomb of the Kings, walks in the Troodos Mountains and it maybe warm enough for the beach. Worth considering if you want the best shot at decent January weather.

Your profile says you like hiking, walking, touring cathedrals & old homes + good food - Malta has all of that in spades. English is widely spoken and the people are welcoming and helpful - they'll be thrilled if you say please & thank you in Maltese. The buses are easy to use, as are the taxis and ferries.

Lovely churches are literally everywhere - on both Malta & Gozo. The most famous is the over-the-top Baroque Co-Cathedral in Valletta with two Caravaggio's, but we love the much less well known Church of St. Paul Shipwreck dating from 1582 just as much, if not more (since we had it all to ourselves).

Casa Rocca Piccola in Valletta is a lovely aristocratic home open for tours that include a visit to the underground air raid shelter from WWII - accessed via the garden.

Hiking & walking opportunities abound (we go in May for the wildflowers) - esp. on Gozo.

If you enjoy history, Malta is a great destination as it has a bit of everything: prehistoric temples, Roman era, the Knights of St. John, and WWII. My husband and I have been twice (both in May) - the first visit was ten nights (7 in Valletta, 3 Gozo), the second visit was 7 nights (again split between Valletta & Gozo) - and we're planning another visit for 2022. I'm 1/4 Maltese, so I'm biased, but for a history aficionado like my DH, it's full of interesting sights and things to do. The bonus of winter is it won't be crowded.

Good food is not difficult to find if you're willing to do a bit of research. If you decide to go, I can give restaurant recommendations. My husband and I went on a Rural Food & Wine Tasting Tour run by Merrill EcoTours that was truly excellent. The owner is passionate about preserving and supporting Malta's rural farms and culture. He can put together a custom tour or choose from one on their website. I highly recommend a full day excursion with them.

As others have mentioned, Malta can be damp in the winter, so If you rent an apartment, make sure there's heat and ask if it's included.

The Brandt Guide for Malta & Gozo by Juliet Rix is the best guide book out there.