Which of Magic's 1v1 tournament constructed formats is most popular?
In my answer I only discuss the large, official tournaments like Pro Tours and Grand Prix, since they are the only ones with readily available data. Everyone can register a sanctioned event of their own, and there doesn't seem to be an overview with attendance numbers or format used. The best numbers to obtain would probably come from WotC's own market research, but they're never going to publish that in any detail.

In terms of all-time number of events and players, Grand Prix are the most important event type. Perhaps unsurprisingly, Limited and Standard are the most common formats, accounting for 446 of total 654 GPs.


Limited: 290 events, 294,076 players
Standard: 156 events, 172,203 players
Modern: 76 events, 115,227 players
Legacy: 31 events, 47,223 players
Pioneer: 5 events (3 played, 2 planned), 4276 players
Vintage does not have any GP or PT events.


Going by average number of attendees per event, the ranking looks almost inverted:


Legacy: 1,523
Modern: 1,516
Pioneer 1,425
Standard: 1,103
Limited: 1,014


The inversion in ranking of the non-Pioneer formats from total numbers to average numbers per event seems to show that the less-supported formats still have a dedicated player base that makes use of any opportunity to play competitively, while the more supported formats spread out their player base over more events.

Pioneer meanwhile does show a strong popularity, going by average number of players per event. Since it's a brand-new format with all events played in 2020, only time will tell if its popularity is sustainable, or if it's just due the novelty of the format that will eventually wear off.

Pro Tours are harder to quantify by format since they are mostly played in mixed formats, but since their total numbers are much lower and proportionally similar to GPs, they don't change the overall picture. Combinations of Standard and Limited formats account for the plurality of players and events.

In terms of prize pool, however, PTs are much more significant. GPs range from $10K to $80K, while PTs range from $100K to $850K, an order of magnitude more.

Sources: 

Mtg Pro Tour, List of events

MtG Grand Prix, 
 List of events