I haven't used the iPad 4 at all myself, but here's what I gather:
The iPad 4 uses the A6X chipset. I have an old iPhone 5 at work that we use for testing apps before releasing them to the public and it runs incredibly well on 10.3.3. The iPhone 5 obviously has a smaller screen which gives it an advantage, however it uses the A6 SoC which isn't as powerful as the A6X - in other words, I'm sure the iPad 4 will run as good if not better than the iPhone 5 despite its larger screen.
You can easily downgrade it to 8.4.1 using OdysseusOTA 2 if you're somehow not satisfied with iOS 10. No SHSH or other prerequisites except for a jailbreak which is readily available for 32-bit devices on 10.3.3 - just google Phoenix jailbreak.
I've played around with this tool myself both on the iPad 2 (Wi-fi model) and iPhone 4s - never had any issues with activation and the downgrade is completely untethered, just make sure to read the instructions carefully.
You can also use CoolBooter to dual-boot 10.3.3 with another firmware of your choice, even iOS 6 if you're feeling nostalgic
I've been an iOS user since 2008 when I started out with the iPhone 3G on iPhone OS 2.x and have had a myriad of devices, so in other words I've used every single version including minor updates going all the way from iPhone OS 2 to iOS 11. In my experience, iOS 10 is one of the most solid releases so far. I never experienced any significant bugs even on the GM version. iOS 8 was imo the worst iOS version both in terms of pure performance and system stability. I'd definitely recommend that you try it out! Please do a clean install through iTunes, it really helps with performance on older devices.
On a side note, my primary iPad is an iPad 2 running 9.3.5. I spent some time messing around with the settings and managed to tweak the settings in a way that actually allowed this archaic device to run iOS 9 without any major hiccups. I made a thread a while back where I listed all the tweaks I could think of to improve the device's performance. You might find them useful on your iPad as well. Post can be found here:
https://forums.macrumors.com/threads/any-ipad-2-users-still-out-there.2097260/ Usually, Safari can be somewhat problematic on older devices running modern firmwares. The iPad 4 still has a pretty good SoC so if you're having minor performance issues with Safari on 10.3.3, I'd try disabling some features such as pre-loading top search hits, safari suggestions and so on. You could even disable JavaScript though it will cause many web pages to not render properly. If it's really bad, grab Puffin from the App Store - the interface is nowhere near as pretty as Safari but it's a dozen faster than safari on my iPad 2 and really breathed new life into the device.
Hope this helps. Good luck