I'd guess that Ukraine is succeeding, given the Oryx list losses over the past week are predominantly Russian, and most Russian losses are likely not public yet. If Ukraine were failing the list would be full of Ukrainian losses just like when the Russian invasion failed in March the list filled with Russian losses.
I think it is stupid that Russia is trying to hold Kherson. It is such an obviously losing position, and has no strategic value I can think of since they weren't able to advance farther. It is the last serious remnant of their failed February stupidity. You can basically read the sad stories of the Russian survivors now: "the river was low and warm when our unit entered the city across a large bridge in the sunshine. When we left, it was on a barely floating wooden table, the water was deep fast and cold, and the snowflakes were heavier than the shells that were falling all around our unit which already had only 20% of its men surviving." Do Russians not read? Cause anyone who has read anything would have known that sentence would emerge two months ago. I think their strategist slept through Strategy 101 in addition to reading anything.
Consider a popular children's book Mossflower, second in Brian Jacques Redwall series. Weasels and wildcats occupied the forest years ago, introducing a reign of terror. After a summer and spring of irregular warfare, the mice and moles drive them back to their stronghold on the banks of the river. A conversation of European climate and its effects on river flow in different seasons ensues, and then the mice and moles systematically destroy the supplies and fortifications of the weasels and wildcats first with flooding, and then with long range artillery supplied by a foreigner. Eventually the demoralized wildcats and weasels abandon their armor and float across the river on overturned tables and shutters and are easily killed or captured, with many drowning. So am I saying the Russians demonstrate a much poorer understanding of strategy than is conveyed in popular children's books? Yes, I am definitely saying exactly that.