Do you belong more to souce first or to speakers first school of thought ?

It all matters.  Having said that I don’t think that the emphasis on the source should be what it was 50 years ago because the quality of the sources has improved so much.  Midfi turntables and digital sources sound pretty good these days, as a rule.  I’d rather play a $1000 streamer or turntable through $10K speakers than the reverse 

In regard to this subject,  back in the mid 1980's  I was visiting a Linn Naim dealer who had some articles written regarding audio.  One was called "The Hifi Hierarchy" written by Linn Audio founder Ivor Tiefenbrun.  Here,  Ivor described how the front end of the audio system was the most important part of the system.  More so than its amplification or speakers.  Ivor's rationale was simple enough for this belief. Specifically, that it is impossible for amplification or speakers to correct the deficiencies produced by a source component. As such, Linn Naim dealers would encourage those interested in purchasing a new audio system to focus most of their expenditure on a Linn LP 12 turntable, and then build the rest of their system around the LP 12.    Dealers would often sell LP 12 turntables with Naim Naits and Linn Kan speakers, and then allow their customers to trade in the equipment for full value within one year of the original purchase in order to upgrade to a better Naim amplifier and Linn speakers.  This program worked quite  well during the 1980's and was quite lucrative for both Linn and Naim as well as their exclusive dealer network. Eventually both companies  went their separate ways, but back in the day, they had one of the most successful partnerships in the audio business.  

It's intuitively clear that "high end" speakers can't deliver their promise with "low-fi" sources/amplification, but I have never had that personal experience. Reason: full-range floorstanders, unported yet with good bass extension, were beyond my budget. So, while I could swing $2k amp and $2k preamp, $2k was also my limit for speakers. Only after substantially upgrading the speakers did the system come alive. Same electronics, same room, same configuration. Ever since, I have held to this maxim: never spend more than 60% on any component, upstream or down, than you paid for the speakers. (Well, I already knew the maxim, but couldn't afford to honor it). So, for those who endorse OP's binary framing of the question, I am on the speaker side. 

Interesting responses here, and probably no one correct answer for all situations. Today’s digital front end equipment has been changing and improving rapidly compared to speaker and amplifier technology. Just look at the number of new digital front-end products that manufacturers have released in the past few years and claim to improve on their predecessors.  Also, it is much easier to try different front end components than to cycle 100-pound (or more) speakers and amplifiers in and out of a listening room. However, as many here have said, getting both the front end and the amplification/speaker right is important, as is having a system that is complimentary to the other components, the room, and the listener’s music and sonic preferences. This is really a chicken and egg type question where it is one or the other until the listener achieves a balance that results in their satisfaction.