other brand name that aren't brrs + ys are just basically the same as td trucks. Made in exactly the same way, just, in different factories, or packaged by different people. Sometimes shaped, but, thats mostly aesthetic.
BRR + Ytrucks have many advantages. I'll list all I can think of in order of importance for me.
1) single axle. Td trucks often have the little axle the wheel goes on bend, wobble, or fall out completely. Happened on my td wides soo often. Single axle trucks don't have this problem, as the axle is held in place by the wheels in a way, as well as them being designed on brrs + ys better so they don't come out easily like on td trucks.
2) loose riding is possible. Td trucks I find wobble and fall apart if you have them anything but tight. I don't like my brrs uber loose, but, looser than what I can have td trucks.
3) more pop. Because of point 2 above, they don't loose pop when ridden loose.
4) turning. Again with loose trucks, they centre themselves after turning rather than staying lopsided, so your ride is always centred and nice.
5) Better to grind on. The material slides WAYY nicer than on td trucks.
6) kingpin doesn't stick out. On td trucks the kingpin gets in the way of grinding. Doesn't happen on brrs/ys.
7) Looks. Lets face it, td trucks are the most horrible shape. BRRs look pretty much like indy skate trucks, and Ys pretty similar to destructo and/or royal skate trucks.
8 ) No need to tune. TDs need special new bushings, pivot cups, sometimes kingpins and bearing screws are used.. all that is WAYY too fiddly for me.
9) Easy to set up and use. Coupled with above point, td need fiddling around, brrs and ys you just screw the wheels on and roll away smooth.
Hope thats answered your question