Argentina or Portugal ?

Erm... There are very few similarities between the two countries!
My initial reaction is that May is not a good season for Patagonia, which is one of the main draws of a trip to Argentina, although there are other worthy highlights.
Also, Argentina is a huge country and ideally needs several weeks, whereas a 7-10 day trip already gives a good sample of Portugal.

We were advised by locals to go to Argentina early March, no later. Huge country. If you go, do The Lakes Crossing out of Bariloche.

I’ve only been to Buenos Aires and loved it. We spent a week there back in September 2016. We’d love to return to visit other parts of the country. The weather was spectacular when we were there.
Haven’t spent much time in Portugal for decades, but it isn’t nearly the size of Argentina. Either country is a good choice.

Both countries are wonderful, but that is like comparing Pennsylvania to Texas.

For South America, I suggest Around the Horn cruises that go from Buenos Aires to Chile. Plan on a few days in BA prior to your cruise.

Have been to both countries and loved them. I was in Argentina in May and spent six nights in Buenos Aires and four nights in Mendoza that included a day in the Andes and it was priceless. Hopefully I’ll return and visit Bariloche. However, I don’t know what Bariloche would be like in May considering it is in the lakes region but it would be gorgeous to see. If you plan on going to Patagonia I suggest going earlier in the year.
I’ve been to Portugal twice and love that country too. I can’t make a recommendation so I suggest trying to pinpoint what you want to see and do and when is the best time to go.

Thank you for all of your replies. Very helpful, We appreciate it!