Without limited options for backup and cross-device migration, I don't use Signal for anything too important, so search is less important.

Whatsapp UI and search are OK but if you have a very long chat history then simple things like jumping to a specific date are difficult. I end up guessing a medium-to-rare search term and using the search history to jump back.

I'd much prefer having control of the data with simple export to my own device for my own search/analysis, but none of these apps do it.

Very good in my experience for WhatsApp.

In the new multi-device beta, desktop clients only sync about a year's worth of messages, though. Not sure if this will change in the final product.