I did both Ancestry and 23andme. The results as to background were broadly the same but Ancestry was a lot more specific. Even right down to one specific county in the southwest of England (you can tell that my ancestors didn't move about much).
One thing I will say is that if you can get either or both of your parents (if they are still alive) to also do a DNA test then that will help a lot as you are going back one generation earlier which makes it a lot easier to find DNA matches.
Between them, my mum and dad have more than double the number of matches that I do and since I know that they are my real parents that means that all of these matches are also my DNA matches as well.
With changing names etc that makes life more difficult but Ancestry is much better for sorting this out.
Just to give one example. A woman on 23andme was shown as being related to me quite closely but I had never heard of her. We got talking and it turned out that her mother and aunt had both been adopted at an early age and she was interested in finding out who her mother's birth parents (maternal grandparents) were.
23andme can't help with that but Ancestry can (with a bit of help from FindMyPast as well).
So I did some digging and found the following:
It turns out that the grandmother was born in County Galway, Ireland and then married while she was living in Wexford.
Her husband was a policeman who had recently returned from China where he had served for six years in the Shanghai Municipal Police (many Shanghai policemen at this time were Irish or British).
After marrying, they then relocated to what is nowadays Kenya where he joined the British East African Mounted Police based in Nairobi. Unfortunately he died two years later and her grandmother returned to the UK.
About five years after his death, her grandmother gave birth to two daughters (my relative’s mother and aunt) in London and they were both adopted at an early age.
They had earlier been fostered and were shown on the 1921 Census as foster children.
Normally, if a woman was unmarried then no father would be shown on the birth certificate. But in both cases her widowed grandmother gave the name of her (five year) deceased husband as the father.
In reality, given the DNA test, it appears that it is some relation of mine (likely from my grandparent's or great grandparent's generation) that was the father.
I’m still working on exactly which relative of mine might have been her grandfather but my best guess at the moment is a man who was the cousin of my great grandfather.
All this came from searching the records available on Ancestry (and also FindMyPast which has the 1921 Census)
Also, you don't have to sign up for an annual subscription, you can do it for just 3 months or even one month at a time.