I have a Stokke Xplory and absolutely love it and thoroughly recommend it. But that's because we don't own a car and our Xplory lives in our front room un-collapsed!
In the 18 months we've had it, we've only put it in a car boot a few times and found it to be bulky and the seat unit needs to be separated from the chassis (although this is a quick process) We had it in an Astra, so quite generous boot, but not loads of room left after the Xplory was in there.
With regards to going up stairs, the Xplory does have the 2 wheel option, but it is recommended that you don't do this with a child in the seat. It is however very narrow, so the width shouldn't be an issue. The Bee is 3kg lighter than the Xplory though and also pretty narrow. I personally wouldn't feel happy carrying a child up stairs in any pushchair. Especially in the early days\weeks (childbirth can do you in and you're likely to be prone to back strain). If your intention is to take baby up first then come back for the pushchair, the 2 wheel option of the Stokke distributes the weight in such a way that it would mitigate any weight difference.
As we are travel almost entirely on foot, I find the Xplory to be perfect. At 21 months my son still faces me. The height factor is the best thing: my son is able to interact with people around him. We talk all the time as I walk. His language skills are very advanced (I'm sure this is in part down to the Xplory). Now he wants to walk a lot of the time, the Xplory is easy to manouevre one-handed. Oh, and the shopping bag fits a gargantuan load!
The reason I chanced upon your message is that I'm now considering purchasing another pushchair. At 21 months, my son is fast approaching the 15kg weight limit of the Xplory (and most other strollers). Due to the price of the Xplory we don't really want to risk overloading it, as we intend to use it for subsequent children (or at least sell it on!). As the Bee has a weight limit of 17.5kg, and is rear facing, it is now my potential next pushchair.
Due to weight and size the Bee may be a better option for your needs, but to be honest if you bought a Stokke I'm sure you wouldn't regret it.
I agree about buying second hand (we originally had a second hand Buzz, but I was never quite happy with it) and when I decided I had enough money to get an Xplory, I knew it would have to be new. However, both Xplory and Bee have great resale values, so that's worth noting!
Sorry it's so long, but hope this helps.