I am in a similar situation with a mid 2010 8 Core 2.4 Ghz and I've not bothered to upgrade it beyond adding 32 gigs of ram, an SSD and a faster graphics card, so it could run Mojave. I resisted the temptation of a move to Catalina, figuring that if it needs patches to update it will always be a risk.
Looking at this in practical terms I believe Intel stopped issuing security updates for these about a year ago and Apple are likely to stop issuing security updates for Mojave in just over a year from now. There are other issues like not being able to enable file vault, while air drop is hamstrung, so yes this is an outdated machine, albeit one I rather admire after years of wonderful service. It's still a great workhorse.
For the last year my plan has been to keep going with the Mac Pro until they come out with minis using the new Arm processors, which at a guess will be about a year from now. This all seemed to make sense, but I am in two minds now, because there may well be a bug laden transition period with third party software adapting to the new processors and I need this for work. On the other hand I tend to keep computers for a long time without trading them in and who wants to be stuck with a fairly new Intel mini when all the attention jumps to Arm?
What I can tell you is that a friend with a maxed out top spec 2010 Mac Pro massively prefers the mini and tells me it runs beautifully. Already for the last year or so I have found system updates on the Mac Pro very hit and miss with frequent problems, which I suspect is down to the new video card and the Samsung SSD. I cannot even run disk utility in recovery mode and I'm generally fed up with some of the obvious problems that come from running an outdated machine. I can't even boot into safe mode without reinstalling the original graphics card.
My father was using an entry level 2012 Mac mini that is horrendously slow, but I cannot fault it for reliability, which goes a long way towards reassuring me that running a mini instead of a Mac Pro would not be something to worry about from that perspective. A few weeks ago he purchased an entry level i3 mini with 8 gigs of ram and a 256gig drive. I only used it for a few minutes around the finder and Safari, but I was honestly shocked at how smooth and fast it was.
After returning home I checked out the benchmarks online and the single core performance was almost twice as fast as my Mac Pro. It was whisper quiet, noticeably faster loading web pages and really forced me to acknowledge that the old beast was really just old now. When I looked at multicore performance my Mac Pro was still faster, but only by about 5% and we are comparing it here to an i3... I think one of the new i7 minis would out perform the Mac Pro for most purposes, except perhaps 4K video editing without an external card.
I don't know what your Mac Pro would be worth, but I think prices have been tumbling ever since the new mini was introduced and I've seen some exchanging hands at shockingly low prices lately as we all come to similar conclusions. I am private beta testing some software at the moment and if I mention something is slow I'm told it is probably down to my legacy hardware, which Apple deemed obsolete sometime ago now.
My thought is to buy a new mini (not sure when) and then keep the Mac Pro on Mojave for a while as a backup that is restricted to offline tasks like video editing to bypass potential security issues or running 32-bit apps. When the intel mini is a few years old that will become the backup and I'll buy an Arm based mini.