I have only played without Bonds once. The group was made up of some of my 'core' (meaning people I play with regularly, who love character interaction and are active, make sure to share the spotlight but still interested and always engaged) and some random people from LFG. It was also a short thing, only three sessions... so take all of this with that in mind.
What you can lose with bonds is essentially a part of the roleplay. Bonds intentionially incentivise interacting with other PCs and while my 'core' still did this anyway because that is what they enjoy, the random people weren't interested or rather reciprocating.
Also their characters seemed more inconsistent (but that also might be because, well, random people), interacting with the others mainly because of the last thing the other character did rather than what their bonds would have maybe told them about each other.
And last but not least, except for one of my core again, every PC was friendly to every other one because there was no incentive (especially for the new people) to make things interesting between the PCs.
For my regular campaign I use bonds because I don't play only with my core group and I want to keep incentivising actually stopping to think about how your character feels about another character... what defines the relationship between the two, and whether or not that changed significantly after each session.