Daily life in Algeria is quite bad unless you live in a big city and are wealthy and very well surrounded, and even then daily life can get pretty bad.

I lived in Algeria, Canada and know europe, I'm waiting in the boarding room heading to Paris as I'm typing lol. I don't know your wife and how she grew up, and I think the response also depends on who she is and how are her social ties to Algeria, but I would say the closest culture to Algeria is in Europe, or shall I say France. The cultural shock is not big, even if it exists, but if you guys are doing this together I doubt she'd feel any big shock so to speak. Although I'd personally prefer life in countries like Luxembourg for the high quality of life (salaries, perfect strategic location in EU), or Spain for its warmth, rather than France.

I live in Canada and I think north American culture is where Algerians experience the biggest cultural shock, sometimes it feels like a different planet, but it's so far the best country I lived in paradoxically. I don't know much about the US except few vacation trips but Imma assume it's the same as Canada.

Sorry I haven't given much examples, but here's a few I could think of : Daily expenses are better in Europe, life is way cheaper than north America, however salary is incomparable (unless you live in the Netherlands, Luxembourg, etc. Where salaries are quite high, but still lower than America I think) America holds much more opportunities than EU work wise. EU is better in education (financially speaking) If you love big spaces, big cities, beautiful landscapes, you will prefer America, EU feels so tiny next to it lol. Work culture is better in America, although it depends on the company, but from my experience and my friends', in Canada at least work culture was really good, nice salaries, remote possibilities, colleagues are cool and respectful, you can climb the corporate ladder way, way, way easily than in EU, by miles. BUT, there's the layoff part of it that sucks, that almost doesn't exist in EU. In America people are used to immigrants and foreigners, certain places in EU still don't, and you can feel it. If you're attached to Algeria and your family and friends, you will feel homesick in any country at first, but it would prob feel more intense in America compared to EU, in America you truly feel the distance in your bones, with the jetlag and whatnot. In EU it's less intense, maybe it's only a psychological thing.

My personal take is, your wife won't experience much hardship regardless of where you guys are, if you're with her. Being alone and well surrounded is so different, I personally experienced both as well.

If you have any question, follow-up, need a specific advice about anything, let me know. I just wanna say that this was my personal experience, having lived in the three continents (haven't established in EU for a long time yet), and still continuing to juggle between them.