I don't know of anyone who has compared a large set of Russian words with Ukrainian words but theoretically one could compare two dictionaries with tens of thousands of words. Most of the comparisons are between a set of 10 to 200 words.
The answer above by @Follower compares such a set of words. Another comparison is elinguistics.net by Vincent Beaufils which compares 18 words and comes up with 4.8 genetic distance:
English | Ukrainian | Russian | Points
-----------+---------------------------+----------------------------+-------
Death | -S-M-R-T- Smert' (смерть) | -S-M-R-T- Smjert' (Смерть) | 100,00
Ear | -V-KH- Vukho (вухо) | -KH- Ukho (Ухо) | 50,00
Eye | -K- Oko (око) | -K- Oko (Око) | 100,00
Four | -CH-T-R- Chotiri (чотири) | -CH-T-R- Chetiri (Четыре) | 100,00
Hand | -R-K- Ruka (рука) | -R-K- Ruka (Рука) | 100,00
I | -J- Ya (Я) | -J- Ja (Я) | 100,00
Name | -M- Imya (ім'я) | -M- Imja (Имя) | 100,00
Night | -N-CH- Nich (ніч) | -N-CH- Noch (Ночь) | 100,00
Nose | -N-S- Nis (ніс) | -N-S- Nos (нос) | 100,00
Sun | -S-N-C- Sontse (Сонце) | -S-L-N-C- Solnce (Солнце) | 75,00
Three | -T-R- Tri (три) | -T-R- Tri (Три) | 100,00
Tongue | -J-Z-K- Yazik (язик) | -J-Z-K- Jazyk (Язык) | 100,00
Tooth | -Z-B- Zub (зуб) | -Z-B- Zub (зуб) | 100,00
Two | -D-V- Dva (два) | -D-V- Dva (Два) | 100,00
Water | -V-D- Voda (вода) | -V-D- Voda (Вода) | 100,00
Who | -KH-T- Khto (хто) | -K-T- Kto (Кто) | 88,64
Wind | -V-T-R- Viter (вітер) | -V-T-R- Veter (ветер) | 100,00
You (thou) | -T- Ti (ти) | -T- Ty (Ты) | 100,00
Analysis:
Total Points/#words: 1713,64/18 (=95,202/100). This value has to be reverted (100-Result) to get the Genetic distance:
Genetic distance: 4,80
These langages are very closely related!
Period Ukrainian: Year 2000, Period Russian: Year 2000.