Here's a nice comparison from ThePointsGuy:
https://thepointsguy.com/credit-cards/showdown-amex-platinum-vs-delta-reserve/
Test run a few itineraries to the places you're traveling to in the future to help you decide. Unless Delta offers the most convenient, and cheapest, flights to a majority of your and your husband's destinations, I'd select the Amex cc to give me freedom to choose the airline that offered the best itinerary. Ideally, you'll find a direct flight, or a layover with just enough time to go to make your next flight, negating the need for a lounge altogether.
Years ago, we started traveling extensively to the Caribbean and I did zero research before paying $$$ for a Delta platinum cc. Too late I realized that USAir had the best AND cheapest flights from my location. Since that costly mistake, I've switched to Chase Sapphire Reserve card rather than being committed to one airline.
The last few years, we've traveled extensively to Europe and always fly biz class, which includes lounge access, so I have a bit of experience using them. Honestly, I only find them truly valuable for long layovers, or if my flight is delayed extensively. If I am fortunate enough to book a direct flight, I don't use them at all:
1) If your airport has them, they're often off the beaten path, hard to find, and not necessarily close to your gate.
2) Even if I dutifully arrive 2 hours before my domestic flight, after getting through TSA, I'm lucky if I have enough time to sit down at all, let alone make my way to the lounge to score a free bagel before the flight starts boarding 30-45 minutes before departure time.
3 Even if I dutifully arrive 3 hours before my international flight, the lounges at my airport close at 7pm, before I have a chance to use it.
4) They can get crowded, esp in the middle of peak travel times.
That being said, for long layovers or delays, it is nice to have a more comfortable place to spend for a few hours and grab a bite to eat. How much is that worth? Only you can answer that.
To answer your specific questions: Usually the secondary cardholder gets lounge access for a fee, or free if they are traveling with the primary cardholder only.
If your husband flies more than you, definitely put the card in his name and make yourself the companion. Of course, if it helps him bump up a status, only he will be eligible for upgrades to First Class. Then you can test your marriage!
If it matters to you, AMEX is not widely accepted in Europe.
Hope this helps. Happy travels!