I tested with both LivingDNA and 23 & Me, and both confirmed my same Y H2, and Mtdna H1c3 Haplogroups. I think they are both using similar tools, but have different visual interpretations. Regarding my Y H2 DNA Haplogroup, it is rare, and I only have the main identifying downstream 'P96' subclade confirmed by both, so I cannot move from that at this time.
In my case the actual results between them are not too far apart . In regard to my Autosomal makeup results, both confirm 100% European, with LivingDNA, 100% British and Irish, and 23 & Me 98% North West European, so not too far apart. I only tested with two different companies basically to have my results compared and confirmed.
The actual Haplogroup origins are a bit vague by both,in my opinion, as I just think they don't know.
23 & Me, do seem to want more of your results shared, and do offer to give a lot more personal health related information, if you accept or consent to their conditions.