I'd probably keep them as separate sites and strategically interlink them assuming there is enough potential profit to justify the effort.

I imagine that both sites are getting traffic for different keywords (widgets & sprockets) which you would endanger if you combined the sites. Merging the sites might also end up losing some backlinks. If an outside site is currently linking to both of your sites, they might remove one of the links when you redirect the site. Having two sites that are branded separately, also doubles the chances of developing partnerships. Some people might not like your current site but would be open to another site approaching them. Having two sites also gives you double chances to rank on the first page That will require extra work to build up the backlinks for both sites but there will also be some economies of scale. You can also test out different SEO tactics like schema or fresh content to see what works best. If you have the budget & time, developing both domains can ultimately lead to the most traffic. Be honest with yourself. If you don't have the time or money, then only go after one site otherwise you will fall short with both sites.

If you go with one domain, as you already mentioned go with 301, and try to map equivalent pages together. This can be tricky with very large sites. Keep the redirects in place for years.

Thank you for these insights. Much appreciated.

15 months ago I decided to merge two global widget sites,there were no duplicate widgets but they were using two totally different self-made css templates, it simply took a couple of months of very hard work ensuring all was good to go and on merging day it was a simple htaccess 301 upload and immediately it was all working perfectly. There were several thousand pages plus a minimum 6-10 images on each page. Every page was built manually, every image manually optimised.

What was the result? Within a couple of weeks G had it all indeced, rankings were retained and in many cases improved plus over the ensuing months until March 2021 when many sites experienced strange Google things. Even now the increase in traffic is more than the two separate sites. Current rankings are superb.

However, insofar as my sites are concerned, I am now considering splitting them for business reasons I do not wish to go into other than I am looking at 10-20 years ahead. This will be a simple job to do.

Decide early on which domain name to use and ensure it reflects that through the entire site.
I assume it will be built in html 5 responsive?
How many people will be working on this melding? One or a team? If it's a team ensure all are on-board as to what is going on otherwise big mistakes will happen.
Check that htaccess 301 several times over ... and then again.
Do not forget the site map.
If you use social media ensure all those correspond to the "new" site.
Any questions, just ask, I'll see if I know!

From experience I can tell you new questions may arise daily but once you get going it does all fall into place relatively easy however it may seem daunting at the beginning.

One huge bonus I found was with updating absolutely everything was how much cleaner the code and directory structure is.