Hahaha, well I suppose I should be happy that you've changed your position from Archeopteryx is "just a bird" all the way to Archeopteryx is "just a bird with unique features". I guess that's progress.
;)
But, if we're being honest, it's NOT just a bird with unique features is it? It's a "bird" with features that are inherently reptilian. It's a "bird" with the exact sort of features we would expect to see during a speciation event in which "birds" were much more like their dinosaur precursors.
Not only that, if you'll recall, you were the one to bring up morphological and anatomical differences. I'm not sure it's really fair to cry foul (or perhaps, in this case, fowl) now that it's "too subjective" a topic since you've decided you don't like where the evidence is leading.
But all that's neither here nor there. To you're broader point, we have a multitude of mechanism for looking at and measuring the difference in species. We can do this in several different ways:
1.) Mitochondrial DNA
2.) X Chromosomes
3.) Endogenous Retrovirus'
4.) Allele Frequencies
These are each independent methods of studying various aspects our DNA to determine hierarchy. For example, evolution predicts that our closest cousins are chimpanzees', followed by guerrillas and then orangutans. And when we look at our mitochondrial DNA (this is what's used in paternity and ancestry tests) we observe the exact same thing.
The same is true when we look at the family lines along the x-chromosome. We find that human's closest cousins are chimpanzees followed by guerrillas and then orangutans.
Next, we can do something very different. We can see what endogenous retrovirus' (ERVs) we share with other animals. According to evolution, we should expect that any ERVs we share with orangutans we'd also share with guerrillas and chimpanzees since orangutans are our most distant ape cousins. And, conversely, we'd expect that there would be some ERVs we'd share with chimpanzees and guerrillas that we don't share with orangutans. Guess what? This is exactly what we observe!
Lastly, we can look at allele frequencies (or, more broadly, genotype frequencies). And the species with which humans have the lowest number of genetic variants is . . . you guessed it, chimpanzees! Wow, what a stunning surprise. Want to wager which species might be next closest? Or next closest after that? Why guerrillas and orangutans of course!
So there we have it, four independent methods of studying DNA that all converge on the exact same hierarchy. But we don't have to stop there. There's a host of other methods we can use too!
5.) Homologous Structures
6.) Vestiges
7.) Atavisms
8.) Phylogenetic Heterogeneity
9.) Allopatric Speciation
. . .
And want to guess the hierarchy at which all these methods also arrive?
This is an important point. There's not just lot's of evidence for evolution. There's lot's of methodologies that all converge on the same answer. In science, having two independent methods reaching a similar conclusion is generally considered rock solid. In biology, evolution doesn't just have two. There at least nine that I know of (and I'd not be surprised if there are even more).
In closing, I'd like to mention I don't think there's anything wrong with your skepticism (a demand for evidence). So long as you stay true to the flip side of that coin as well - keeping an open mind (aka - following that evidence where it leads).