Saw your other thread in setting up solr on Windows platform and thought about making a suggestion, but decided to wait.
Now that you've asked this question, think you can answer some yourself - once you setup simple search.
Solr requirements add more complexity - as you have experienced already.
An apache extension - solr - has to be installed.
Then there is the Solr server itself - java based - admin interface runs on a non-protected port - thus increasing the attack surface of your Moodle server. Matter of fact, a flaw in Log4J affected Solr thus Solr Search in Moodle a year or so ago.
Solr search is more accurate as to what it indexes.
Brief history of Solr in Moodle ... around version 1.7 of Moodle (if I recall correctly) Solr search was first introduced. It was removed from core in 1.8 (the next release of Moodle) and wasn't considered again until somewhere in series 3.
Simple search is just that - very appropriately named. Easier to setup and run but the results it produces are not as accurate as Solr.
My 2 cents ...
Depending upon what courses are offered on your Moodle - paid or free or whatever, any search that finds something in a course that's not open to the public or a paid course, could beget you, the admin person, more support questions - user typical question ... how come I can't access X. Or a prof being asked to open up their course, etc.
So, if you were asking for votes, I'd vote for 'simple' knowing it's limitations! 
I'd even consider not running search at all on some servers!
You could 'open to Google' and let Google crawl your site - but like the old Google Applicance, could find too much!
'SoS', Ken