Silly question, but here it goes.
Which would be most ideal for a 6 acre property with long driveway, mature trees, snow removal, and making and maintaining a small veggie garden. A midsize backhoe with loader or a midsize tractor with backhoe and loader?
I would go with around 35-45 Ag Tractor with backhoe and FEL, if you only foresee occasional small digging jobs.
With the PTO on an AG tractor you can use a variety of implements, like snow blower, 3 point mower, post digger, grading blade, rototiller, cultivator, mulcher etc. many of which could be very useful, if not necessary on 6 acres. Note that these backhoes are best suited to dig simple small jobs like a trench for pipes or cleaning a ditch and things like that
You do need to consider some things carefully though.
If you are planning to do a lot of digging you might end up frustrated with a few things. First the reach of the boom is about 8ft on these tractor backhoes and mostly 180 degrees rotations. So if you have to dig a narrow trench 4ft deep, say with a 12inch bucket, you will likely run out of space to dispose of the excavated material.
That always has been my issue with the one I had. (1999 NH TC33 Boomer)
When you select models you need to make sure to get one that has a sub-frame and with quick and easy installation procedure. On mine (with a sub-frame) installing or removing was a 5 minutes tool-less job (after some practice). Only 2 pins to install and the hoses to connect.
That becomes extremely important if you want to be able to use your other implements painlessly.
Typically I would have my backhoe on just for digging jobs and had a weight box on the 3-point for when the backhoe was off, as it is safer to use the FEL with a counterweight when the backhoe isn't on.
In hindsight though, (hindsight is 20/20) I would have gone with an Ag tractor with FEL without backhoe and used the backhoe money to get a mini excavator. Like 2-3 tons with rubber tracks and a blade.
That would leave your PTO and 3-points hitch free on the Ag tractor and a mini excavator of that size will outperform all small tractors backhoes. The fact that it can dump the material around a 360 circle is a huge difference.