SUTs are tricky and they do have advantages.
The tricky bit is they have to be loaded correctly. Many SUTs are meant to be used with a specific cartridge; such SUTs as a result are meant to be loaded at their output by the 47K input impedance of the phono section (47K is the standard for phono input sections).
If the loading is different, for example the load is a higher impedance, the transformer can 'ring' (distort) and so will sound brighter. This can also happen if a different cartidge, with a difference source impedance is used. Transformers are call that because they transform impedance and this goes both ways: I can't be more emphatic that transformers do not isolate impedance!
Jensen Transformers makes very high quality SUTs and have several models, some meant to be used with tubes and others with solid state. Because they have a generic quality, to deal with the loading problem Jensen has published a chart that shows what resistor/capacitor combination should be at its output so as to prevent ringing.
The advantage of SUTs are several. First, they contribute almost no Johnson noise at all (which would be heard as hiss otherwise) and so can benefit both tube and solid state phono sections if a LOMC cartridge is being used. This is the most obvious benefit.
The next benefit is that SUTs, being transformers, allow you to run the input and/or output balanced or single-ended. In this manner you can minimize the sonic artifact that is caused by the tonearm cable; so those of you that spent a lot of money on the tonearm cable take note: if you also run an SUT you can go balanced from the phono cartridge (which is a balanced source) and so get better performance from the cable, which is arguably the most important place in the audio system that the cable really be right. Any place further downstream will not be able to make up for any deficiencies or colorations imposed by the cable! You can do this even if your phono section has a single-ended input.
Finally, SUTs usually do not have bandwidth much past 100KHz. For this reason, they can effectively block the RFI that is usually caused by the cartridge inductance being in parallel with the capacitance of the tonearm cable. People that don't use SUTs often resort to 'cartridge loading' resistors to get rid of the distortion caused by this problem, although they usually think they are tuning out brightness. What they don't realize is that the brightness is the result of distortion. Take away the RFI and the overload it causes to the phono section and the brightness is gone.
I've written plenty about the adverse effects 'cartridge loading' can cause and will not repeat myself here.
For those that don't use an SUT though, the RFI generated must be dealt with; its my theory that the reason there is an SUT vs direct in debate (for those of you who have preamps that have sufficient gain) has to do with whether the RFI is dealt with properly when running direct-in.
IME, most designers of phono sections do not take the phenomena of the electrical resonance/RFI problem of LOMC cartridges into account in their designs, so the design has problems with high frequency overload as result. But if that problem is dealt with, usually a phono section that can run direct-in will sound more transparent than using an SUT. This is simply because there won't be additional distortion.
In a nutshell what I'm saying is if you need the gain because your phono section only does high output cartridges, this is a good way to go. It might sound better than a poorly designed high gain phono section as well. But if the phono section is properly designed it goes the other way!
Ultimately the designer/dealer or whatever likely isn't going to tell you what's up with all this; IME if they don't know about the cartridge electrical resonance issue you'll get snowed. So you just have to try it and see what works.
And in case its not obvious, keep the interconnect cable capacitance as low as possible. This means don't use regular interconnects not meant for use with a phono cartridge!
