Obviously a limited budget must make compromises. Even the best transformer, perfectly tuned, will reduce peak amplitudes, flatten waveforms and lose low level detail; it's an inevitable consequence of passing an electrical signal by induction. OTOH, a HOMC also reduces peak amplitudes, flattens waveforms and loses low level detail, but for mechanical reasons rather than electrical ones. (The third choice, an LOMC + inexpensive active gain device will also compromise the sound, though in different ways depending on the device.)
Which is least bad? As usual, it comes down choosing the sonic compromises which work best for your ears and system. You can do this the easy but potentially expensive way (buy different stuff and compare) or the hard but less expensive way (develop a strong internal sense of what sounds right, figure out why, then move continuously toward equipment that brings you closer to that goal for reasons you understand). There's no prefab answer to your question IMO. :-(
SOTA is a different matter. It cannot be attained with any transformer we've heard (5 or 6 in all). Core saturation is one audible problem, though it can be somewhat reduced with good materials. Ultrasonic ringing and its audible zone harmonics are another, though they can be tamed with a Zoebel network. What can't be eliminated are the reduction in peak amplitudes, flattening of waveforms and loss of low level detail. Once the rest of a system reaches a certain level these effects become noticeable, especially if you have a SOTA high gain phono stage handy to compare.
