Group comparison - aggregate data or compare means? Let’s say I measure a parameter of interest out of a group of 10 genetically identical individuals (e.g., an inbred C57BL/6J mouse). I can compute a mean, SD or 95% CI from that sample. Then let’s say I get another group of 10 animals that are slightly different from the first group but still I consider them very similar (e.g., same species but from a different geographical location or a different vendor). Let’s say I repeat this 5 times, so I have 5 n=10 readings (so either 50 total or 5 means, each from one of the n=10 samples). That’s my group A.
Now, I do the same with a different animal (e.g. inbred BALB/c mice), now generating 5x10 individual readouts or 5 means, each from one of the samples. That’s my group B.
I want to know if there’s a statistical difference between those two groups, null hypothesis being that there is no difference.
How to perform this group comparison? I was thinking about calculating 95% confidence intervals from the pooled sample of 50 and compare using CI. Or, should one compute the mean from each sample (after all, the mean can still vary from one sample to the other regardless of the genetic similarly between groups) and then analyze variance and ask for significance under p<0.05? (Assuming Gaussian distribution of the A and B population).

First, let's clarify terminology, because you use 'group' to refer to 'genetically identical mice' and also to refer to a 'different animal'. That's confusing. Let's instead call a set of genetically identical mice clones and different animals species (it doesn't matter if they are a different species or not, but distinguishing between these two levels is important).
You have 3 options open to you that I can think of.
A linear mixed-effects model is a common way to model this type of data. They tend to work best if you have more groups (clones) though, but 5 might be just about enough to make this approach work.
Generalised Estimating Equations is an alternate approach, and I think it is  simpler. GEEs work well when you are only interested in population-level patterns (in this case, if you don't care about variation within clones).
Possibly even simpler is to fit a standard linear model but use clustered standard errors. I know less about this and so can't comment with confidence about this approach. But apparently hypothesis testing becomes a little more complicated.
My sense is that GEEs already capture most of the benefits of robust standard errors while also being more flexible, so I would probably use GEEs or mixed-effects models. When to use generalized estimating equations vs. mixed effects models? provides good advice on when to use the two different approaches. McNeish et al. 2017 is a longer but very readable discussion about all 3 methods.
