You shouldn't need to install any software, just switch on screen sharing and remote login in your system preferences.
Presumably that option works ok with "Screens"? It appears that Splashtop does need its own server installed, & in fact probably uses extensions to VNC, or is completely proprietary, as it transfers audio as well, even keeping in sync with the video

Additionally, it auto adjust the mac's screen resolution, & restores it on exit.
I see Screens is rather dearer than Splashtop, so if it appears on sale sometime, I'll try it out. Splashtop also works fine on the rare occasions I need to connect to Windows, & for the price seems good value.
Interestingly, using Splashtop has been the first time I've thought a bluetooth keyboard could be handy on an iPad, as the on-screen keyboard "pushes up" the target screen so half of it is blocked when entering characters. However, even just having a BT keyboard connected gives the facility of a single line of useful keypresses available to touch at the very bottom of the screen, which isn't intrusive.
As there are so many vnc clients available, I suppose ultimately, it depends what features the OP is looking for .........