Here are the core county populations of a few "major" Florida cities in the late 19th century and early 20th century. While Pensacola (Escambia) was more of a peer during the reconstruction period, Tampa (Hillsborough) had become the main peer by 1900, primarily due to its port, phosphate, cigars, and the Spanish-American War. Hillsborough passed Duval in population the first decade of the 20th century before having a "setback" with part of the county splitting to form Pinellas (St. Petersburg/Clearwater). Miami-Dade rapidly caught everyone and never looked back after the Great Depression. I believe it's hard to prove that Jax was considerably more economically influential than Tampa at any point in the 20th century and Miami after WWII. By the same token, during the immediate decades following the Civil War, I'm not so sure it was "significantly" more influential than Pensacola. Go back before than and we'd have to start considering the city we lost....Mobile.
1880
19,431 Duval
12,156 Escambia
10,940 Monroe
5,814 Hillsborough
1890
26,800 Duval
20,188 Escambia
18,006 Monroe
14,941 Hillsborough
861 Miami-Dade
1900
39,733 Duval
36,013 Hillsborough
28,313 Escambia
18,006 Monroe
4,955 Miami-Dade
1910
78,374 Hillsborough
75,163 Duval County
38,029 Escambia
21,563 Monroe
11,933 Miami-Dade
1920
113,540 Duval
88,257 Hillsborough (Pinellas succeeded from Hillsborough in 1912)
49,386 Escambia
42,753 Miami-Dade
28,265 Pinellas
19,550 Monroe
1930
155,503 Duval
153,519 Hillsborough
142,955 Miami-Dade
62,149 Pinellas
53,594 Escambia
13,624 Monroe
1940
267,739 Miami-Dade
210,143 Duval
180,148 Hillsborough
159,249 Pinellas
74,667 Escambia
14,078 Monroe