I spent several weeks in Ukraine last year, between late May and mid-June. After doing a lot of research I decided I needed twice as much time in Kyiv as in L'viv because of the number of museums I was interested in. Accordingly, that's the way I allocated my time. I had over a week in K'yiv.
My major period of interest is the 20th century. The Chernobyl Museum and the Famine (Holodomor) Museum in K'yiv were very accesible to English-speakers. I especially recommend watching the subtitled videos of survivors of the famine. There's also a good introductory film at that museum; be sure the staff realize you're an English speaker so they run the right version for you. I think knowing something about the famine is critical; it seems to affect the country's psyche to this day.
Kyiv's WWII Museum is also good, but it has a fair amount of material (mostly the human-interest stuff) that hasn't been translated into English. Still worthwhile.
There are lovely churches in K'yiv--I'd say more than in L'viv. But L'viv has a greater density of beautiful architecture since it didn't take the wartime battering Kyiv received.
Rather than splitting my time and using a good chunk of a day to change cities and hotels, I'd choose one or the other. Splitting 4 days will give you a really inadequate amount of time in both places, I believe. Assuming you're going to.l Krakow on this trip, I'd suggest making Kyiv your Ukrainian stop.
Because of my interests, I spent less time in the touristy parts of Kyiv than most foreigners do. I didn't find any oppressive crowds. I didn't feel unsafe anywhere, but the public transportation can be massively crowded. I wouldn't attempt it with luggage.
The core of L'viv was much more touristy than central Kyiv. Folks who say L'viv is "the next Krakow" may not have been to L'viv recently.
Edited to add: Carry a scarf around with you for popping into churches. I don't know whether they'd throw you out without one, but the local women consistently don them--to the point that you sonetimes see loaners on a counter inside a church.