It all comes down a lot of the time to preferences that make no more sense than the people who argue about Ford vs. Chevy vs. Dodge.
Personally, I really do NOT like Blue Bird buses. I don't like the eyebrows over the side windows (with a lot of hard road use the body twisting and flexing can cause the sheet metal to tear in the corners of the eyebrows), every single one with which I have been involved with rattled more when brand new than any Thomas or IC bus did when old enough to take out of service. And they new conventional they call the Vision is more like no-vision and I really do NOT like the dash layout and ergonomics.
Thomas has always made a good bus but the C3's have had a LOT of electrical issues.
IC/AmTrans/Ward have suffered over the years due to quality control. The last of the Wards and the first of the AmTrans were really pretty bad. Once IC opened up their Tulsa Bus Plant they got quality control taken care of pretty well. But then they started having engine issues.
In regards to engines you will discover the same sort of prejudices when it comes to choosing engines. Cummins and IHC engines that are inline and not V-engines have great reputations. The V-type engines over the years have been disappointing to say the least. Cat engines are okay but they tend to be expensive to maintain and you have to go to a Cat shop to get them fixed. Mercedes-Benz and the Brazilian Ford are okay engines but it can be extremely difficult and expensive to find qualified people who will work on them. Finding parts for them can be difficult at best, expensive always, and rarely close to where you might be. Freightliner dealers really do NOT like to see buses driving in their doors. They particularly don't like it when they see the M-B engine logo on the hood.
In regards to transmissions, 99% of all buses have had automatic transmissions for more than 20-years. Finding one with a factory installed stick shift is almost unknown. They are out there but be resigned to the fact most will have an automatic. The vast majority of buses came with Allison automatics. The preferred ones are the newer ones with five and six gears with at least one OD gear. Older ones came with four with the odd one out there having a 5-speed automatic. The AT500 series were inexpensive and designed for low HP/Torque and normally had no lock up ability. The most common school bus transmission was the MT600 series. They came in all sorts of different versions including some that had a deep low first gear or a hydraulic retarder built into the transmission. The MT-series all had lock up in the 3rd and 4th gears. The HT700 series was found on only the heavy duty buses with the big HP engines like the Cummins Big Cam or Detroit -92 series engines. The HT series locked up in all gears except 1st.
Some of the newer buses might be found with a Voith or ZF transmission. There isn't anything really wrong with them. In fact those that have them really like them. But unless you happen to know someone in a large city transit bus shop finding anyone who knows anything about a Voith or where to get parts for one is pretty much a non-starter. The ZT isn't quite as bad but they are much more difficult to find parts and service than an Allison.
Good luck and happy trails to you!