Okay, How Important Is Speaker Break In? (Dynaudio Contour 60i)

It’s not about break-in, it’s about finding the right position in your room for the new speakers. Besides, why would the Dyn’s be a major upgrade to your Bowers? 

I had a pair of Dynaudio Contour 60's.  Like you, I had a very good deal on them.  Based on demo's of other dynaudio products, slightly lower priced I figured I would love them (as they had to be even better...since they cost more).  I didn't love the lower priced ones, but liked them, and hey... for this price it has to be a bargain!

I will tell you, more than any other speaker I have owned I did feel they broke in.  Dyn says they can measure it.  

I liked them, but never truly loved them.  I felt for a 10k retail speaker - I needed to pretty much love them.

The bass was great, the mids were good, the tweeter was good.  But for me, they always sounded closed in.  I tried adjusting room treatments, upgraded electronics (which I wanted to do anyways).  

But, I never loved those speakers. In fact I liked some much lower priced, used, beat to crap speakers better (they weren't better, but I found myself listening to those more and more).  

Sold the Dyn's, and never regretted it.  They were good, but at 10k retail, I want to LIKE the speaker a lot.  When I demo Dyn's in stores from time to time I still like them (though I haven't demo'd the contours again).  

I do find it interesting how quickly they did a full overhaul of the Contour Series.  But, you have those and don't love them.  

Based on past experience, if I were in your shoes - I would flip them.  Doesn't mean they are bad, just not for you.

I replaced a set of B&W 803s speakers with a pair of Focal Kanta 3s.  Took a while to sort through some music I thought was good but much better sound right out of the box.

Break in is important but only in the first few hours; if you don't like the speakers after a day or two, send it back. I purposely tried to gauge this when I bought Special 40s. Significant change in the first minutes, then slightly improvements to the 5th hour, then very little to the 15th hour (which btw is the break in time for BWs according to their manual), then next to nothing in the 50th, 100th, 200th playing hours. 
In your case though, it might be more of your preference of the BW house sound which makes the contour less impressive; haven't heard the matrix but the more modern BWs are slightly boosted up top and below, while the Dyns are dull flat. Do try to see if you can like the Dyn sound as they should be more detailed, albeit less exciting.

I had the Contour 20s for a short time. Strange animal. They were used and several hundred hours broke in according to the owner. Never quite got along with them. They sounded great ish sometimes with some music but overall not my cuppa tea. 

Had the Dyn Docua 140s years ago and everything sounded good on those although not spectacular