try the $2 type first.
Just to share. TLDR (too long don't read)
I have tried both active & passive antennas.
Summary: If antenna can be placed at good/ideal position -- active antenna does not have much advantage over the passive antenna.
The passive antenna I tried is the cheapo $2 type antenna that Gregory (usually) ask people to try first:
I bought a K2 DVB-T2 digital TV receiver set top box (STB) -- used by many other people:
My K2 DVB-T2 STB is placed in front of my TV -- which is (actually) not too far away (2-3m) from the window.
The cheapo $2 passive antenna can't view/receive Mediacorp DVB-T2 channels properly -- if placed next to the TV.
The cable length of the cheapo $2 passive antenna is (only) about 1m -- not long enough for me to place the passive antenna at the window.
So I bought a 2m coaxial extension cable:
Using the coaxial extension cable, I'm now able to place the cheapo $2 antenna at the window.
To my (pleasant) surprise, when using the cheapo $2 antenna placed at the window, I can receive all Mediacorp DVB-T2 channels properly. Moreover, signal quality of some channels (e.g. Ch 5) can be as high as 90% !!
The point I want to make is that -- if can placed at good/ideal location -- even cheapo $2 antenna can work.
Above correlates to why Gregory (usually) advise people to try the cheapo $2 antenna first.