The LPC is definitely more relevant to commercial firms. The SQE, particularly in my experience with BPP, is very 'high street'. It is unfortunate that the LPC is pretty much no more, given the value of the elective modules which cover areas of far greater relevance to commercial in-house and private practice.
I understand some law firms are having their trainees complete an "SQE+" course which they've pulled together with these providers to give insight into these areas and provide a useful "top up". I haven't yet seen this is available to those self funding, but I would not be surprised if this changes in future. I'm in-house but was lucky to have a pretty frank and open discussion with the SQE coordinator at one of the large firms we work with and this was very much the message from her too. If I could've done the LPC, I certainly would've and feel it would've been of far greater utility, but at the end of the day - both reach the end goal of qualification. Hope that helps!