If a summon was available, I'd use it. My logic is that the designers gave me access to these tools, why not?
Having said that, the Nameless Puppet is the only fight where you don't get the summon - so that's the one time the designers expect you to "git gud".
Great fight, the hardest I've ever seen in a Souls-like, but technically fair. Just gotta learn those parry timings, yo.
Nameless Puppet was definitely harder than Isshin, in my opinion.
Isshin was tough but very fairly designed. Part of NP's moveset in Phase 2 is a bit gimmicky and hard to dodge/block, which is a bit of a pain.
I think Isshin is easier only in that it's a better designed fight that rewards you more for learning his moves and tells.